Recent zbMATH articles in MSC 81https://www.zbmath.org/atom/cc/812021-02-27T13:50:00+00:00WerkzeugEdge contraction on dual ribbon graphs and 2D TQFT.https://www.zbmath.org/1453.141342021-02-27T13:50:00+00:00"Dumitrescu, Olivia"https://www.zbmath.org/authors/?q=ai:dumitrescu.olivia"Mulase, Motohico"https://www.zbmath.org/authors/?q=ai:mulase.motohicoSummary: We present a new set of axioms for 2D TQFT formulated on the category of cell graphs with edge-contraction operations as morphisms. We construct a functor from this category to the endofunctor category consisting of Frobenius algebras. Edge-contraction operations correspond to natural transformations of endofunctors, which are compatible with the Frobenius algebra structure. Given a Frobenius algebra \(A\), every cell graph determines an element of the symmetric tensor algebra defined over the dual space \(A^\ast\). We show that the edge-contraction axioms make this assignment depending only on the topological type of the cell graph, but not on the graph itself. Thus the functor generates the TQFT corresponding to \(A\).Book review of: J. Bricmont, Making sense of quantum mechanics.https://www.zbmath.org/1453.000082021-02-27T13:50:00+00:00"Kiessling, Michael K.-H."https://www.zbmath.org/authors/?q=ai:kiessling.michael-karl-heinzReview of [Zbl 06508042].Collective synchronization of the multi-component Gross-Pitaevskii-Lohe system.https://www.zbmath.org/1453.350272021-02-27T13:50:00+00:00"Bao, Weizhu"https://www.zbmath.org/authors/?q=ai:bao.weizhu"Ha, Seung-Yeal"https://www.zbmath.org/authors/?q=ai:ha.seung-yeal"Kim, Dohyun"https://www.zbmath.org/authors/?q=ai:kim.dohyun"Tang, Qinglin"https://www.zbmath.org/authors/?q=ai:tang.qinglinSummary: In this paper, we propose a multi-component Gross-Pitaevskii-Lohe (GPL for brevity) system in which quantum units interact with each other such that collective behaviors can emerge asymptotically. We introduce several sufficient frameworks leading to complete and practical synchronizations in terms of system parameters and initial data. For the modeling of interaction matrices we classify them into three types (fully identical, weakly identical and heterogeneous) and present emergent behaviors correspond to each interaction matrix. More precisely, for the fully identical case in which all components are same, we expect the emergence of the complete synchronization with exponential convergence rate. On the other hand for the remaining two interaction matrices, we can only show that the practical synchronization occurs under well-prepared initial frameworks. For instance, we assume that a coupling strength is sufficiently large and perturbation of an interaction matrix is sufficiently small. Regarding the practical synchronization estimates, due to the possible blow-up of a solution at infinity, we a priori assume that the \(L^4\)-norm of a solution is bounded on any finite time interval. In our analytical estimates, two-point correlation function approach will play a key role to derive synchronization estimates. We also provide several numerical simulations using time splitting Crank-Nicolson spectral method and compare them with our analytical results.\( \mu \)-norm of an operator.https://www.zbmath.org/1453.810202021-02-27T13:50:00+00:00"Treschev, D. V."https://www.zbmath.org/authors/?q=ai:treshchev.dmitrij-vSummary: Let \((\mathcal{X},\mu)\) be a measure space. For any measurable set \(Y\subset\mathcal{X}\) let \(1_Y: \mathcal{X}\to\mathbb{R}\) be the indicator of \(Y\) and let \(\pi_Y\) be the orthogonal projection \(L^2(\mathcal{X})\ni f\mapsto \pi_Y f = 1_Y f\). For any bounded operator \(W\) on \(L^2(\mathcal{X},\mu)\) we define its \(\mu \)-norm \(\|W\|_\mu = \inf_\chi\sqrt{\sum\mu(Y_j)\|W\pi_Y\|^2}\), where the infimum is taken over all measurable partitions \(\chi=\{Y_1,\dots,Y_J\}\) of \(\mathcal{X}\). We present some properties of the \(\mu \)-norm and some computations. Our main motivation is the problem of constructing a quantum entropy.Construction of an equivalent energy-dependent potential by a Taylor series expansion.https://www.zbmath.org/1453.810622021-02-27T13:50:00+00:00"Behera, A. K."https://www.zbmath.org/authors/?q=ai:behera.amiya-kumar|behera.abhisek-k"Khirali, B."https://www.zbmath.org/authors/?q=ai:khirali.b"Laha, U."https://www.zbmath.org/authors/?q=ai:laha.ujjwal"Bhoi, J."https://www.zbmath.org/authors/?q=ai:bhoi.jSummary: To construct a phase-equivalent energy-dependent local potential corresponding to a sum of local and nonlocal interactions, we use a simple method for expanding the wave function in a Taylor series up to the third order. We apply the constructed potentials to calculate the scattering phase shifts using the phase equation. The results for scattering in nucleon-nucleon, \( \alpha \)-nucleon, and \(\alpha-\alpha\) systems agree reasonably well with the standard data.Nonlinear radion interactions.https://www.zbmath.org/1453.810612021-02-27T13:50:00+00:00"Volobuev, I. P."https://www.zbmath.org/authors/?q=ai:volobuev.igor-p"Keizerov, S. I."https://www.zbmath.org/authors/?q=ai:keizerov.s-i"Rakhmetov, E. R."https://www.zbmath.org/authors/?q=ai:rakhmetov.e-rSummary: We consider the Randall-Sundrum model with two branes in which the fields of the Standard Model are localized on the brane with negative tension and the gravitational field and an additional stabilizing scalar Goldberg-Wise field propagate in the space between the branes. We construct a Lagrangian for scalar fluctuations of the gravitational and scalar fields against the background solution. We obtain an effective four-dimensional Lagrangian describing nonlinear self-coupling terms of the scalar radion field in a polynomial approximation up to the fourth order and also nonlinear terms of the coupling of the radion and Standard Model fields. We estimate possible values of the self-coupling constant.Vertical D4-D2-D0 bound states on \(K3\) fibrations and modularity.https://www.zbmath.org/1453.141012021-02-27T13:50:00+00:00"Bouchard, Vincent"https://www.zbmath.org/authors/?q=ai:bouchard.vincent"Creutzig, Thomas"https://www.zbmath.org/authors/?q=ai:creutzig.thomas"Diaconescu, Duiliu-Emanuel"https://www.zbmath.org/authors/?q=ai:diaconescu.duiliu-emanuel"Doran, Charles"https://www.zbmath.org/authors/?q=ai:doran.charles-f"Quigley, Callum"https://www.zbmath.org/authors/?q=ai:quigley.callum"Sheshmani, Artan"https://www.zbmath.org/authors/?q=ai:sheshmani.artanSummary: An explicit formula is derived for the generating function of vertical D4-D2-D0 bound states on smooth \(K3\) fibered Calabi-Yau threefolds, generalizing previous results of \textit{A. Gholampour} and \textit{A. Sheshmani} [Adv. Math. 326, 79--107 (2018; Zbl 1386.14193); Adv. Theor. Math. Phys. 19, No. 3, 673--699 (2015; Zbl 1333.81242)]. It is also shown that this formula satisfies strong modularity properties, as predicted by string theory. This leads to a new construction of vector valued modular forms which exhibit some of the features of a generalized Hecke transform.Binary relations, Bäcklund transformations, and wave packet propagation.https://www.zbmath.org/1453.810222021-02-27T13:50:00+00:00"Zharinov, V. V."https://www.zbmath.org/authors/?q=ai:zharinov.victor-vSummary: We propose a mathematical apparatus based on binary relations that expands the possibility of traditional analysis applied to problems in mathematical and theoretical physics. We illustrate the general constructions with examples with an algebraic description of Bäcklund transformations of nonlinear systems of partial differential equations and the dynamics of wave packet propagation.Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra.https://www.zbmath.org/1453.810402021-02-27T13:50:00+00:00"Stukopin, V. A."https://www.zbmath.org/authors/?q=ai:stukopin.vladimir-alekseevichSummary: Using the approach developed by Gautam and Toledano Laredo, we introduce analogues of the category \(\mathfrak{O}\) for representations of the Yangian \(Y_{\hbar}(A(m,n))\) of a special linear Lie superalgebra and the quantum loop superalgebra \(U_q(LA(m,n))\). We investigate the relation between them and conjecture that these categories are equivalent.Quantum anomalies via differential properties of Lebesgue-Feynman generalized measures.https://www.zbmath.org/1453.810312021-02-27T13:50:00+00:00"Gough, John E."https://www.zbmath.org/authors/?q=ai:gough.john-e"Ratiu, Tudor S."https://www.zbmath.org/authors/?q=ai:ratiu.tudor-stefan"Smolyanov, Oleg G."https://www.zbmath.org/authors/?q=ai:smolyanov.oleg-georgievichSummary: We address the problem concerning the origin of quantum anomalies, which has been the source of disagreement in the literature. Our approach is novel as it is based on the differentiability properties of families of generalized measures. To this end, we introduce a space of test functions over a locally convex topological vector space, and define the concept of logarithmic derivatives of the corresponding generalized measures. In particular, we show that quantum anomalies are readily understood in terms of the differential properties of the Lebesgue-Feynman generalized measures (equivalently, of the Feynman path integrals). We formulate a precise definition for quantum anomalies in these terms.Hurwitz numbers from Feynman diagrams.https://www.zbmath.org/1453.810522021-02-27T13:50:00+00:00"Natanzon, S. M."https://www.zbmath.org/authors/?q=ai:natanzon.sergei-m"Orlov, A. Yu."https://www.zbmath.org/authors/?q=ai:orlov.aleksandr-yuSummary: To obtain a generating function of the most general form for Hurwitz numbers with an arbitrary base surface and arbitrary ramification profiles, we consider a matrix model constructed according to a graph on an oriented connected surface \(\Sigma\) with no boundary. The vertices of this graph, called stars, are small discs, and the graph itself is a clean dessin d'enfants. We insert source matrices in boundary segments of each disc. Their product determines the monodromy matrix for a given star, whose spectrum is called the star spectrum. The surface \(\Sigma\) consists of glued maps, and each map corresponds to the product of random matrices and source matrices. Wick pairing corresponds to gluing the set of maps into the surface, and an additional insertion of a special tau function in the integration measure corresponds to gluing in Möbius strips. We calculate the matrix integral as a Feynman power series in which the star spectral data play the role of coupling constants, and the coefficients of this power series are just Hurwitz numbers. They determine the number of coverings of \(\Sigma \) (or its extensions to a Klein surface obtained by inserting Möbius strips) for any given set of ramification profiles at the vertices of the graph. We focus on a combinatorial description of the matrix integral. The Hurwitz number is equal to the number of Feynman diagrams of a certain type divided by the order of the automorphism group of the graph.Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: general analysis and simplest examples.https://www.zbmath.org/1453.810172021-02-27T13:50:00+00:00"Matveev, V. B."https://www.zbmath.org/authors/?q=ai:matveev.vladimir-b"Smirnov, A. O."https://www.zbmath.org/authors/?q=ai:smirnov.alexander-oSummary: We consider nonlocal symmetries that all or all even (all odd) equations of the AKNS hierarchy have. We construct examples of solutions simultaneously satisfying several nonlocal equations of the AKNS hierarchy. We present a detailed study of single-phase solutions.Centers of generalized reflection equation algebras.https://www.zbmath.org/1453.810392021-02-27T13:50:00+00:00"Gurevich, D. I."https://www.zbmath.org/authors/?q=ai:gurevich.dmitrii-i"Saponov, P. A."https://www.zbmath.org/authors/?q=ai:saponov.pavel-aSummary: As is known, in the reflection equation (RE) algebra associated with an involutive or Hecke \(R\)-matrix, the elements \(\operatorname{Tr}_RL^k\) (called quantum power sums) are central. Here, \(L\) is the generating matrix of this algebra, and \(\operatorname{Tr}_R\) is the operation of taking the \(R\)-trace associated with a given \(R\)-matrix. We consider the problem of whether this is true in certain RE-like algebras depending on a spectral parameter. We mainly study algebras similar to those introduced by Reshetikhin and Semenov-Tian-Shansky (we call them algebras of RS type). These algebras are defined using some current \(R\)-matrices (i.e., depending on parameters) arising from involutive and Hecke \(R\)-matrices by so-called Baxterization. In algebras of RS type. we define quantum power sums and show that the lowest quantum power sum is central iff the value of the ``charge'' \(c\) in its definition takes a critical value. This critical value depends on the bi-rank \((m|n)\) of the initial \(R\)-matrix. Moreover, if the bi-rank is equal to \((m|m)\) and the charge \(c\) has a critical value, then all quantum power sums are central.Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra.https://www.zbmath.org/1453.810362021-02-27T13:50:00+00:00"Todorov, Ivan"https://www.zbmath.org/authors/?q=ai:todorov.ivan-t"Dubois-Violette, Michel"https://www.zbmath.org/authors/?q=ai:dubois-violette.michelConstruction of the Dirac operator on the \(q\)-deformed quantum space \(EAdS^2\) using a generalized \(q\)-deformed Ginsparg-Wilson algebra.https://www.zbmath.org/1453.810162021-02-27T13:50:00+00:00"Lotfizadeh, M."https://www.zbmath.org/authors/?q=ai:lotfizadeh.m"Feyzi, R."https://www.zbmath.org/authors/?q=ai:feyzi.rSummary: We construct \(q\)-deformed Dirac and chirality operators on the \(q\)-deformed quantum space \(EAdS^2\) using a generalized quantum Ginsparg-Wilson algebra. We show that in the limit \(q\to1\), these operators become the Dirac and chirality operators on the undeformed quantum space \(EAdS^2\).On the uniqueness of invariant states.https://www.zbmath.org/1453.810352021-02-27T13:50:00+00:00"Bambozzi, Federico"https://www.zbmath.org/authors/?q=ai:bambozzi.federico"Murro, Simone"https://www.zbmath.org/authors/?q=ai:murro.simoneIn many cases the quantum physical system is endowed with an action by a group of \(*\)-automorphisms which is not compact nor abelian, even if it acts ergodically. An example is the abelian Chern- Simons theory. In this case the general criterion for the existence and uniqueness of invariant states is still missing. However in [\textit{F. Bambozzi} et al., ``Invariant states on noncommutative tori'', Preprint, \url{arXiv:1802.02487}] ``invariant states by the symplectic group of automorphisms on group algebras with involutions that define irrational non-commutative tori have been classified using elementary, and mostly algebraic, methods.More precisely, it was shown that for irrational rotational algebras the only state invariant under the action of the symplectic group is the canonical trace state''.
The present paper continues the mentioned paper. The main result is the following one. ``Given an abelian group \(G\) endowed with a \(T=\mathbb{R}/\mathbb{Z}\)-pre-symplectic form, the authors assign to it a symplectic twisted group \(*\)-algebra \(W_G\) and then provide criteria for the uniqueness of states invariant under the ergodic action of the symplectic group of automorphism''
Reviewer: Dmitry Artamonov (Moskva)Analytical and combinatorial aspects of the eigenproblem for the two-magnon sector of XXX Heisenberg rings.https://www.zbmath.org/1453.820112021-02-27T13:50:00+00:00"Krasoń, P."https://www.zbmath.org/authors/?q=ai:krason.piotr"Łabuz, M."https://www.zbmath.org/authors/?q=ai:labuz.miroslaw"Milewski, J."https://www.zbmath.org/authors/?q=ai:milewski.janSummary: In this paper we study both analytical and combinatorial properties of solutions of the eigenproblem for the Heisenberg \(s\)-\(1/2\) model for two deviations. Our analysis uses Chebyshev polynomials, inverse Bethe Ansatz, winding numbers and rigged string configurations. We show some combinatorial aspects of strings in a geometric way. We discuss some exceptions from the connection between the combinatorial nature of an eigenstate and the analytical type of a solution of the eigenproblem. In particular, as an illustration of the aforementioned exceptions, we analyze the singularities of Bethe parameters for bound states at the border of the Brillouin zone.Ground states of two-component Bose-Einstein condensates passing an obstacle.https://www.zbmath.org/1453.820022021-02-27T13:50:00+00:00"Xu, Liangshun"https://www.zbmath.org/authors/?q=ai:xu.liangshunSummary: This paper is concerned with two-component Bose-Einstein condensates with both attractive intraspecies and interspecies interactions passing an obstacle in a plane, which can be described by the ground states of the nonlinear Schrödinger system defined in an exterior domain \(\Omega = \mathbb{R}^2 \backslash \omega \), with \(\omega \subset \mathbb{R}^2\) being a bounded smooth convex domain. Under the assumption that the trapping potentials \(V_i(x)\) for \(i = 1, 2\) attain their global minima only on the whole boundary \(\partial \Omega \), the existence, non-existence, and limiting behavior of ground states for the system are studied. When intraspecies interactions \(a_1\) and \(a_2\) satisfy \(0 < a_1, a_2 < a\)* and interspecies interaction \(\beta\) satisfies \(0 < \beta < \beta \)* by the delicate energy analysis, an optimal blow-up rate for ground states is also given as \(\beta \nearrow \beta \)*, where \(\beta^* = a^* + \sqrt{(a^* - a_1)(a^* - a_2)}\), \(a^* := \| Q \|_2^2\), and \(Q\) is the unique positive solution of \(\Delta Q - Q + Q^3 = 0\) in \(\mathbb{R}^2\).
{\copyright 2020 American Institute of Physics}Long-range interactions in cold atomic systems: a foreword.https://www.zbmath.org/1453.820572021-02-27T13:50:00+00:00"Morigi, Giovanna"https://www.zbmath.org/authors/?q=ai:morigi.giovannaFor the entire collection see [Zbl 1175.70003].Analysis of the discrete Spectrum of the family SPECTRUM of \(3\times 3\) operator matrices.https://www.zbmath.org/1453.810292021-02-27T13:50:00+00:00"Muminov, Mukhiddin I."https://www.zbmath.org/authors/?q=ai:muminov.mukhiddin-i"Rasulov, Tulkin H."https://www.zbmath.org/authors/?q=ai:rasulov.tulkin-khusenovich"Tosheva, Nargiza A."https://www.zbmath.org/authors/?q=ai:tosheva.nargiza-aSummary: We consider the family of \(3\times 3\) operator matrices \(\mathbf{H}(K)\), \(K\in\mathbb{T}^3:=(-\pi; \pi]^3\) associated with the lattice systems describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. We find a finite set \(\Lambda\subset\mathbb{T}^3\) to prove the existence of infinitely many eigenvalues of \(\mathbf{H}(K)\) for all \(K\in\Lambda\) when the associated Friedrichs model has a zero energy resonance. It is found that for every \(K\in\Lambda\), the number \(N(K, z)\) of eigenvalues of \(\mathbf{H}(K)\) lying on the left of \(z, z<0\), satisfies the asymptotic relation \(\lim\limits_{z\to -0}N(K,z)|\log|z||^{-1}=\mathcal{U}_0\) with \(0<\mathcal{U}_0<\infty\), independently on the cardinality of \(\Lambda\). Moreover, we prove that for any \(K\in\Lambda\) the operator \(\mathbf{H}(K)\) has a finite number of negative eigenvalues if the associated Friedrichs model has a zero eigenvalue or a zero is the regular type point for positive definite Friedrichs model.Stability and collisions of quantum droplets in \(\mathcal{PT}\)-symmetric dual-core couplers.https://www.zbmath.org/1453.810232021-02-27T13:50:00+00:00"Zhou, Zheng"https://www.zbmath.org/authors/?q=ai:zhou.zheng"Zhu, Bo"https://www.zbmath.org/authors/?q=ai:zhu.bo"Wang, Haibin"https://www.zbmath.org/authors/?q=ai:wang.haibin"Zhong, Honghua"https://www.zbmath.org/authors/?q=ai:zhong.honghuaSummary: We study the effect of the interplay between parity-time \((\mathcal{PT})\) symmetry and optical lattice (OL) potential on dynamics of quantum droplets (QDs) forming in a binary bosonic condensate trapped in a dual-core system. It is found that the stability of symmetric QDs in such non-Hermitian system depends critically on the competition of gain and loss \(\gamma\), inter-core coupling \(\kappa\), and OL potential. In the absence of OL potential, the \(\mathcal{PT}\)-symmetric QDs are unstable against symmetry-breaking perturbations with the increase of the total condensate norm \(N\), and they retrieve the stability at larger \(N\), in the weakly-coupled regime. As expected, the stable region of the \(\mathcal{PT}\)-symmetric QDs shrinks when \(\gamma\) increases, i.e., the \(\mathcal{PT}\) symmetry is prone to break the stability of QDs. There is a critical value of \(\kappa\) beyond which the \(\mathcal{PT}\)-symmetric QDs are entirely stable in the unbroken \(\mathcal{PT}\)-symmetric phase. In the presence of OL potential, the \(\mathcal{PT}\)-symmetric on-site QDs are still stable for relatively small and large values of \(N\). Nevertheless, it is demonstrated that the OL potential can assist stabilization of \(\mathcal{PT}\)-symmetric on-site QDs for some moderate values of \(N\). On the other hand, it is worth noting that the relatively small \(\mathcal{PT}\)-symmetric off-site QDs are unstable, and only the relatively large ones are stable. Furthermore, collisions between stable \(\mathcal{PT}\)-symmetric QDs are considered too. It is revealed that the slowly moving \(\mathcal{PT}\)-symmetric QDs tend to merge into breathers, while the fast-moving ones display quasi-elastic collision and suffer fragmentation for small and large values of \(N\), respectively.Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background.https://www.zbmath.org/1453.810472021-02-27T13:50:00+00:00"Bogdanov, L. V."https://www.zbmath.org/authors/?q=ai:bogdanov.leonid-vitalevichSummary: We obtain a dispersionless integrable system describing a local form of a general three-dimensional Einstein-Weyl geometry with a Euclidean (positive) signature, construct its matrix extension, and show that it leads to the Bogomolny equations for a non-Abelian monopole on an Einstein-Weyl background. We also consider the corresponding dispersionless integrable hierarchy, its matrix extension, and the dressing scheme.Symmetry, invariance and the structure of matter.https://www.zbmath.org/1453.820822021-02-27T13:50:00+00:00"James, Richard D."https://www.zbmath.org/authors/?q=ai:james.richard-dStatistical equilibrium dynamics.https://www.zbmath.org/1453.820262021-02-27T13:50:00+00:00"Kiessling, Michael K.-H."https://www.zbmath.org/authors/?q=ai:kiessling.michael-karl-heinzSummary: We study the mean-field thermodynamic limit for a class of isolated Newtonian \(N\)-body systems whose Hamiltonian admits several additional integrals of motion. Examples are systems which are isomorphic to plasma models consisting of one specie of charged particles moving in a neutralizing uniform background charge. We find that in the limit of infinitely many particles the stationary ensemble measures with prescribed values of the integrals of motion are supported on the set of maximum entropy solutions of a (time-independent) nonlinear fixed point equation of mean-field type. Each maximum entropy solution of this fixed point equation can in turn be either a static or a stationary solution for the entropy-conserving Vlasov evolution, or even belong to a one-dimensional orbit of maximum entropy solutions which evolve into one another by the Vlasov dynamics. In short, the macrostates of individual members of an equilibrium ensemble are not necessarily themselves in a state of global statistical equilibrium in the strict sense. Yet they are always locally in thermodynamic equilibrium, and always global maximizers of the pertinent maximum entropy principle.
For the entire collection see [Zbl 1175.70003].A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: homogeneous relaxation and transport coefficients.https://www.zbmath.org/1453.653682021-02-27T13:50:00+00:00"Wu, Lei"https://www.zbmath.org/authors/?q=ai:wu.lei.3|wu.lei.1|wu.lei|wu.lei.2|wu.lei.4Summary: A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. The computational cost of the proposed FSM is \(O(M^{d_v - 1} N^{d_v + 1} \log N)\), where \(d_v\) is the dimension of the problem, \(M^{d_v - 1}\) is the number of discrete solid angles, and \(N\) is the number of frequency nodes in each direction. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and momentum/energy to the machine and spectral accuracy, respectively. Based on the variational principle, transport coefficients such as the shear viscosity, thermal conductivity, and diffusion are calculated by the FSM, which agree well with the analytical solutions. Then, the FSM is applied to find the accurate transport coefficients through an iterative scheme for the linearized quantum Boltzmann equation. The shear viscosity and thermal conductivity of three-dimensional quantum Fermi and Bose gases interacting through hard-sphere potential are calculated. For Fermi gas, the relative difference between the accurate and variational transport coefficients increases with fugacity; for Bose gas, the relative difference in thermal conductivity has similar behavior as the gas moves from the classical to degenerate limits, but the relative difference in shear viscosity decreases when the fugacity increases. Finally, the viscosity and diffusion coefficients are calculated for a two-dimensional equal-mole mixture of Fermi gases. When the molecular masses of the two components are the same, our numerical results agree with the variational solutions. However, when the molecular mass ratio is not one, large discrepancies between the accurate and variational results are observed; our results are reliable because (i) the method does not rely on any assumption on the form of velocity distribution function and (ii) the ratio between shear viscosity and entropy density satisfies the minimum bound predicted by the string theory.Quantifying non-gaussianity via the Hellinger distance.https://www.zbmath.org/1453.810112021-02-27T13:50:00+00:00"Zhang, Yue"https://www.zbmath.org/authors/?q=ai:zhang.yue"Luo, Shunlong"https://www.zbmath.org/authors/?q=ai:luo.shunlongSummary: Non-Gaussianity is an important resource for quantum information processing with continuous variables. We introduce a measure of the non-Gaussianity of bosonic field states based on the Hellinger distance and present its basic features. This measure has some natural properties and is easy to compute. We illustrate this measure with typical examples of bosonic field states and compare it with various measures of non-Gaussianity. In particular, we highlight its similarity to and difference from the measure based on the Bures distance (or, equivalently, fidelity).The SK model is infinite step replica symmetry breaking at zero temperature.https://www.zbmath.org/1453.820882021-02-27T13:50:00+00:00"Auffinger, Antonio"https://www.zbmath.org/authors/?q=ai:auffinger.antonio"Chen, Wei-kuo"https://www.zbmath.org/authors/?q=ai:chen.wei-kuo"Zeng, Qiang"https://www.zbmath.org/authors/?q=ai:zeng.qiang|zeng.qiang.1From the introduction: Theorem 1. For any \(\xi\) and \(h\), the mixed \(p\)-spin model at zero temperature is \(FRSB\).
Theorem 3. There exist \(m_{n+1}> m_n\) and \(\eta \in (q_n,1)\) such that \(P(\gamma_q)<P(\gamma)\).Quantum-inspired glowworm swarm optimisation and its application.https://www.zbmath.org/1453.901942021-02-27T13:50:00+00:00"Gao, Hongyuan"https://www.zbmath.org/authors/?q=ai:gao.hongyuan"Du, Yanan"https://www.zbmath.org/authors/?q=ai:du.yanan"Diao, Ming"https://www.zbmath.org/authors/?q=ai:diao.mingSummary: In order to solve discrete optimisation problem, a novel intelligence algorithm called as quantum-inspired glowworm swarm optimisation (QGSO) is proposed. By hybridising the glowworm swarm optimisation, quantum coding and quantum evolutionary theory, the quantum state and binary state of the quantum glowworms can be well evolved by simulated quantum rotation gate. The classical benchmark functions are used to test effectiveness of QGSO. The proposed QGSO algorithm is an effective discrete optimisation algorithm which has better convergent accuracy and speed. Then QGSO is used to resolve thinned array optimisation difficulties. Simulation results are provided to show that the proposed thinned array method based on QGSO is superior to the thinned array methods based on previous classical intelligence algorithms. The proposed thinned array method based on QGSO can search the global optimal solution of thinned array.Static and dynamic coherent robust control for a class of uncertain quantum systems.https://www.zbmath.org/1453.930712021-02-27T13:50:00+00:00"Xiang, Chengdi"https://www.zbmath.org/authors/?q=ai:xiang.chengdi"Petersen, Ian R."https://www.zbmath.org/authors/?q=ai:petersen.ian-r"Dong, Daoyi"https://www.zbmath.org/authors/?q=ai:dong.daoyiConsider a class of open uncertain nominal quantum systems defined in terms of physical quantities $(S,L,H)$. $S$ denotes a scattering matrix which is a matrix of operators on the underlying Hilbert space, a coupling operator $L$ is a vector of operators on the underlying Hilbert space, and a system Hamiltonian $H$ which is a self-adjoint operator on the underlying Hilbert space. The system Hamiltonian $H$ is decomposed as $H=H_1+H_2$, where $H_1$ is a self-adjoint operator on the underlying Hilbert space referred to as the nominal Hamiltonian considered for a known linear system using parameters $(S, L,H)$. $H_2$ is a self-adjoint operator on the underlying Hilbert space referred to as the unknown perturbation Hamiltonian contained in a specific set of Hamiltonians $W$ [\textit{I. R. Petersen} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 370, No. 1979, Article ID 5354--5363 p. (2012; Zbl 1353.81073)]. The goal is to propose two different methods for the design of directly guaranteed cost coherent quantum controller using direct coupling based on parameters $S, L, H$ and also compare their performance. It means to design the controllers not only robustly stabilizing uncertain quantum system, but also guaranteeing a specific level of performance for any specific value of the uncertainty. One is to build a static guaranteed cost controller for uncertain quantum systems by adding controller Hamiltonian with plant variables. That is, the static controller uses the same mode as the nominal system. The other is to build a dynamic quantum controller which is directly coupled to the given system. Different from the static one, the dynamic controller design method introduces another quantum system as desired controller. Thus, the controller variables are different from plant variables. The guaranteed cost coherent controller design is presented in terms of LMI and nonlinear equality conditions. A nonlinear change of variables is used to convert the problem into a rank constrained LMI problem which is solved using an alternating projections algorithm. A numerical example is supplied to illustrate both coherent controller design methods. It includes also a performance comparison between static coherent controller design and dynamic coherent controller design resulting in an improved control performance of a dynamic controller over a static one.
Reviewer: Lubomír Bakule (Praha)Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets.https://www.zbmath.org/1453.941362021-02-27T13:50:00+00:00"Matsumoto, Ryutaroh"https://www.zbmath.org/authors/?q=ai:matsumoto.ryutarohSummary: We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure.Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime.https://www.zbmath.org/1453.652782021-02-27T13:50:00+00:00"Bao, Weizhu"https://www.zbmath.org/authors/?q=ai:bao.weizhu"Zhao, Xiaofei"https://www.zbmath.org/authors/?q=ai:zhao.xiaofeiSummary: Different efficient and accurate numerical methods have recently been proposed and analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter \(\varepsilon \in(0, 1],\) which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e. \(0 < \varepsilon \ll 1\), the solution of the NKGE propagates waves with wavelength at \(O(1)\) and \(O(\varepsilon^2)\) in space and time, respectively, which brings significantly numerical burdens in designing numerical methods. We compare systematically spatial/temporal efficiency and accuracy as well as \(\epsilon\)-resolution (or \(\epsilon\)-scalability) of different numerical methods including finite difference time domain methods, time-splitting method, exponential wave integrator, limit integrator, multiscale time integrator, two-scale formulation method and iterative exponential integrator. Finally, we adopt the multiscale time integrator to study the convergence rates from the NKGE to its limiting models when \(\varepsilon \to 0^+\).Addendum to ``Derivation of \(K\)-matrix reaction theory in a discrete basis formalism''.https://www.zbmath.org/1453.810582021-02-27T13:50:00+00:00"Alhassid, Y."https://www.zbmath.org/authors/?q=ai:alhassid.y"Bertsch, G. F."https://www.zbmath.org/authors/?q=ai:bertsch.george-f"Fanto, P."https://www.zbmath.org/authors/?q=ai:fanto.pAdds a derivation of a useful formula based on the authors' paper [ibid. 419, Article ID 168233, 7 p. (2020; Zbl 1448.81446)].Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems.https://www.zbmath.org/1453.810372021-02-27T13:50:00+00:00"Campoamor-Stursberg, Rutwig"https://www.zbmath.org/authors/?q=ai:campoamor-stursberg.rutwig"Marquette, Ian"https://www.zbmath.org/authors/?q=ai:marquette.ianSummary: The notion of hidden symmetry algebra used in the context of exactly solvable systems (typically a non semisimple Lie algebra) is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By construction, these algebras do not depend on the choice of realizations by vector fields of the underlying Lie algebra, allowing to propose a new approach to analyze polynomial algebras as those subspaces in an enveloping algebra that commute with a given algebraic Hamiltonian. These polynomial algebras play an important role in context of superintegrability, but are still poorly understood from an algebraic point of view. Among the main results, we present finitely generated quadratic algebras of dimensions 4, 5 and 6, as well as cubic algebras of dimensions 3 and 5, and various abelian algebras, all of dimension 3. Based on the observation how superintegrability is associated with exact solvability, we propose a procedure that connects the underlying Lie algebra with algebraic integrals of motion. As the integrals constructed in such way are now independent on the realization, alternative choices of realizations can provide new explicit models with the same symmetry algebra. In this paper, we consider examples of such equivalent Hamiltonians in terms of differential operators for the three cases and connected to the underlying Lie algebra \(\mathfrak{gl}(2,\mathbb{R})\ltimes \mathbb{R}^2\oplus T_1\) as well as to the maximal parabolic subalgebra of \(\mathfrak{gl}(3,\mathbb{R})\). We also point out differences between the enveloping algebra of Lie algebras and the enveloping algebra of the related differential operators realization.Information-theoretic aspects of Werner states.https://www.zbmath.org/1453.810062021-02-27T13:50:00+00:00"Li, Nan"https://www.zbmath.org/authors/?q=ai:li.nan.2|li.nan.1|li.nan.3"Luo, Shunlong"https://www.zbmath.org/authors/?q=ai:luo.shunlong"Sun, Yuan"https://www.zbmath.org/authors/?q=ai:sun.yuanSummary: In a seminal study of quantum states with Einstein-Podolsky-Rosen correlations (entanglement) admitting a hidden-variable model [Phys. Rev. A (3) 40, No. 8, 4277--4281 (1989; Zbl 1371.81145)], \textit{R. F. Werner} introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner-Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.Higher-rank tensor field theory of non-abelian fracton and embeddon.https://www.zbmath.org/1453.810532021-02-27T13:50:00+00:00"Wang, Juven"https://www.zbmath.org/authors/?q=ai:wang.juven"Xu, Kai"https://www.zbmath.org/authors/?q=ai:xu.kaiSummary: We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The ``gauge structure'' can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang-Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle-hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.A unified system for Coleman-de Luccia transitions.https://www.zbmath.org/1453.830082021-02-27T13:50:00+00:00"Eckerle, Kate"https://www.zbmath.org/authors/?q=ai:eckerle.kateSummary: We show that the presence or absence of negative modes associated with the expansion or contraction of Coleman-De Luccia instantons is controlled by the monotonicity properties of a single function parameterized by the tension and two vacuum energies. This approach simplifies and unifies certain aspects of phase transitions between two de Sitter vacua, between two Anti-de Sitter, and between one of each. This strategy may serve as a guide for identifying negative modes in more complicated gravitational theories, for instance supergravity.Fracton phases via exotic higher-form symmetry-breaking.https://www.zbmath.org/1453.810462021-02-27T13:50:00+00:00"Qi, Marvin"https://www.zbmath.org/authors/?q=ai:qi.marvin"Radzihovsky, Leo"https://www.zbmath.org/authors/?q=ai:radzihovsky.leo"Hermele, Michael"https://www.zbmath.org/authors/?q=ai:hermele.michaelSummary: We study \(p\)-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor \(\operatorname{U}(1)\) scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe \(p\)-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. We also give a general discussion on interpreting \(p\)-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.Bogoliubov many-body perturbation theory under constraint.https://www.zbmath.org/1453.810642021-02-27T13:50:00+00:00"Demol, P."https://www.zbmath.org/authors/?q=ai:demol.p"Frosini, M."https://www.zbmath.org/authors/?q=ai:frosini.m"Tichai, A."https://www.zbmath.org/authors/?q=ai:tichai.a"Somà, V."https://www.zbmath.org/authors/?q=ai:soma.v"Duguet, T."https://www.zbmath.org/authors/?q=ai:duguet.tSummary: In order to solve the A-body Schrödinger equation both accurately and efficiently for open-shell nuclei, a novel many-body method coined as Bogoliubov many-body perturbation theory (BMBPT) was recently formalized and applied at low orders. Based on the breaking of \(U(1)\) symmetry associated with particle-number conservation, this perturbation theory must operate under the constraint that the \textit{average} number of particles is self-consistently adjusted at each perturbative order. The corresponding formalism is presently detailed with the goal to characterize the behaviour of the associated Taylor series. BMBPT is, thus, investigated numerically up to high orders at the price of restricting oneself to a small, i.e. schematic, portion of Fock space. While low-order results only differ by 2--3\% from those obtained via a configuration interaction (CI) diagonalization, the series is shown to eventually diverge. The application of a novel resummation method coined as eigenvector continuation further increases the accuracy when built from low-order BMBPT corrections and quickly converges towards the CI result when applied at higher orders. Furthermore, the numerically-costly self-consistent particle number adjustment procedure is shown to be safely bypassed via the use of a computationally cheap \textit{a posteriori} correction method. Eventually, the present work validates the fact that low order BMBPT calculations based on an \textit{a posteriori} (average) particle number correction deliver controlled results and demonstrates that they can be optimally complemented by the eigenvector continuation method to provide results with sub-percent accuracy. This approach is, thus, planned to become a workhorse for realistic \textit{ab initio} calculations of open-shell nuclei in the near future.Quantum field theory with the generalized uncertainty principle. II: Quantum electrodynamics.https://www.zbmath.org/1453.810602021-02-27T13:50:00+00:00"Bosso, Pasquale"https://www.zbmath.org/authors/?q=ai:bosso.pasquale"Das, Saurya"https://www.zbmath.org/authors/?q=ai:das.saurya"Todorinov, Vasil"https://www.zbmath.org/authors/?q=ai:todorinov.vasilSummary: Continuing our earlier work on the application of the Relativistic Generalized Uncertainty Principle (RGUP) to quantum field theories, in this paper we study Quantum Electrodynamics (QED) with minimum length. We obtain expressions for the Lagrangian, Feynman rules and scattering amplitudes of the theory, and discuss their consequences for current and future high energy physics experiments. We hope this will provide an improved window for testing Quantum Gravity effects in the laboratory.Unitarity of quantum tunneling decay for an analytical exact non-Hermitian resonant-state approach.https://www.zbmath.org/1453.810592021-02-27T13:50:00+00:00"García-Calderón, Gastón"https://www.zbmath.org/authors/?q=ai:garcia-calderon.gaston"Romo, Roberto"https://www.zbmath.org/authors/?q=ai:romo.robertoSummary: By using an analytical exact non-Hermitian formalism for quantum tunneling decay that involves the expansion of the decaying wave function as a linear combination of resonant states and transient functions associated with the complex poles of the outgoing Green's function to the problem, it is shown that the integrated decaying probability density in the whole space satisfies unitarity at each value of time.Bound state solution and thermodynamic properties of the screened cosine Kratzer potential under influence of the magnetic field and aharanov-Bohm flux field.https://www.zbmath.org/1453.810182021-02-27T13:50:00+00:00"Purohit, Kaushal R."https://www.zbmath.org/authors/?q=ai:purohit.kaushal-r"Parmar, Rajendrasinh H."https://www.zbmath.org/authors/?q=ai:parmar.rajendrasinh-h"Rai, Ajay Kumar"https://www.zbmath.org/authors/?q=ai:rai.ajay-kumarSummary: In this article, approximate analytical bound state solutions of the Schrödinger equation in two-dimensional space for screened cosine Kratzer potential (SCKP) under the influence of the magnetic field and Aharanov-Bohm flux field have been investigated. We obtained energy eigenvalues and wave functions for SCKP with external fields (magnetic field and Aharanov-Bohm flux field) via parametric Nikiforov-Uvarov (pNU) method using the approximation method suggested by Greene-Aldrich for handling centrifugal barriers. We deduced energy eigenvalues for screened Kratzer potential (SKP) and Hellmann potential (HP) from the obtained energy spectrum of SCKP with an external field. We extended our results in D dimensions for Hellmann potential in the absence of external fields. Thermodynamic properties such as partition function \(Z(\overrightarrow{B},\Phi_{AB},\beta)\), mean energy \(U(\overrightarrow{B},\Phi_{AB},\beta)\), mean free energy \(F(\overrightarrow{B},\Phi_{AB},\beta)\), entropy \(S(\overrightarrow{B},\Phi_{AB},\beta)\), specific heat capacity \(C_s(\overrightarrow{B},\Phi_{AB},\beta)\), magnetization at finite temperature \((\overrightarrow{B},\Phi_{AB},\beta)\) and magnetic susceptibility \(\chi_m(\overrightarrow{B},\Phi_{AB},\beta)\) at finite temperature are presented. The obtained numerical resultsfor SKP and Hellmann potential are in very good agreementwith numerical results available in the literature with and without external fields respectively.Symplectic geometry of unbiasedness and critical points of a potential.https://www.zbmath.org/1453.530742021-02-27T13:50:00+00:00"Bondal, Alexey"https://www.zbmath.org/authors/?q=ai:bondal.alexey-i"Zhdanovskiy, Ilya"https://www.zbmath.org/authors/?q=ai:zhdanovskiy.ilyaSummary: The goal of these notes is to show that the classification problem of algebraically unbiased system of projectors has an interpretation in symplectic geometry. This leads us to a description of the moduli space of algebraically unbiased bases as critical points of a potential function, which is a Laurent polynomial in suitable coordinates. The Newton polytope of the Laurent polynomial is the classical Birkhoff polytope, the set of doubly stochastic matrices. Mirror symmetry interprets the polynomial as a Landau-Ginzburg potential for corresponding Fano variety and relates the symplectic geometry of the variety with systems of unbiased projectors.
For the entire collection see [Zbl 1446.53004].On the tensor structure of modules for compact orbifold vertex operator algebras.https://www.zbmath.org/1453.170172021-02-27T13:50:00+00:00"McRae, Robert"https://www.zbmath.org/authors/?q=ai:mcrae.robertSuppose \(V\) is a vertex operator algebra and \(G\) is a compact Lie group acting faithfully and continuously (and by vertex operator algebra automorphisms) on \(V\); write \(V^G\) for the fixed subalgebra. \textit{C. Dong} et al. provided in [Int. Math. Res. Not. 1996, No. 18, 913--921 (1996; Zbl 0873.17028)] a Schur-Weyl type duality statement: \(V\) is semisimple as a \((V^G \times G)\)-module, and decomposes as \(V = \bigoplus_I V_I \otimes I\), where \(I\) ranges over the irreducible finite-dimensional \(G\)-modules, and \(V_I\) are nonzero distinct irreducible \(V^G\) modules. In particular, this theorem provides an identification of linear semisimple categories between \(\mathrm{Rep}(G)\) and the subcategory \(\mathcal{C}_V \subset \mathrm{Rep}(V^G)\) consisting of direct sums of the \(V_I\)'s.
The main result of the present paper improves this to an identification of braided monoidal categories. (The theorem is proved for arbitrary abelian intertwining algebras, which are a mild generalization of vertex operator algebras.) The only assumption needed is \(V^G\) indeed has a category of modules, containing \(\mathcal{C}_V\), with a braided tensor structure. This assumption is fairly deep in general: except in very special cases (unitary, strongly rational, etc.), the construction of braided tensor category structures on modules for vertex operator algebras requires the sophisticated theory of logarithmic vertex tensor categories developed by \textit{Y.-Z. Huang} and \textit{J. Lepowsky} [J. Phys. A, Math. Theor. 46, No. 49, Article ID 494009, 21 p. (2013; Zbl 1280.81125)], which in turn depends on subtle convergence properties of 4-point functions. Nevertheless, the assumption is known to hold for a vast assortment of examples. The proof uses a nice mixture of vertex-algebraic and tensor-categorical techniques.
Reviewer: Theo Johnson-Freyd (Waterloo)Design of quantum cost efficient reversible multiplier using Reed-Muller expressions.https://www.zbmath.org/1453.941472021-02-27T13:50:00+00:00"Pankaj, N. Rajeev"https://www.zbmath.org/authors/?q=ai:pankaj.n-rajeev"Venugopal, P."https://www.zbmath.org/authors/?q=ai:venugopal.prem|venugopal.priya|venugopal.padmaja"Mortha, Prasanthi"https://www.zbmath.org/authors/?q=ai:mortha.prasanthiSummary: Reversible logic design is one of the emerging trends in recent years as it is good for low power design. A good number of design methods for reversible multipliers were proposed earlier. In this paper, two bit reversible multiplier was designed using Reed-Muller expressions, and this new reversible multiplier was used to design 4-bit reversible multiplier. The results save 16.9\% of quantum cost (QC), 38.5\% of garbage outputs (GOs) and 10.7\% of constant inputs (CIs) compared to earlier designs. The simulations are done on Xilinx 10.1 and are presented. The methodology is extended for the design of 8-bit and 16-bit multipliers and the reversible logic metrics were presented for different bit lengths.Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs.https://www.zbmath.org/1453.650202021-02-27T13:50:00+00:00"Jin, Shi"https://www.zbmath.org/authors/?q=ai:jin.shi"Liu, Liu"https://www.zbmath.org/authors/?q=ai:liu.liu"Russo, Giovanni"https://www.zbmath.org/authors/?q=ai:russo.giovanni.1|russo.giovanni"Zhou, Zhennan"https://www.zbmath.org/authors/?q=ai:zhou.zhennanSummary: In this work, we study the semi-classical limit of the Schrödinger equation with random inputs, and show that the semi-classical Schrödinger equation produces \(O(\varepsilon)\) oscillations in the random variable space. With the Gaussian wave packet transform, the original Schrödinger equation is mapped to an ordinary differential equation (ODE) system for the wave packet parameters coupled with a partial differential equation (PDE) for the quantity \(w\) in rescaled variables. Further, we show that the \(w\) equation does not produce \(\epsilon\) dependent oscillations, and thus it is more amenable for numerical simulations. We propose multi-level sampling strategy in implementing the Gaussian wave packet transform, where in the most costly part, i.e. simulating the \(w\) equation, it is sufficient to use \(\epsilon\) independent samples. We also provide extensive numerical tests as well as meaningful numerical experiments to justify the properties of the numerical algorithm, and hopefully shed light on possible future directions.Classical and quantum Markov processes associated with \(q\)-Bessel operators.https://www.zbmath.org/1453.810452021-02-27T13:50:00+00:00"Bessadok, Khadija"https://www.zbmath.org/authors/?q=ai:bessadok.khadija"Fagnola, Franco"https://www.zbmath.org/authors/?q=ai:fagnola.franco"Hachicha, Skander"https://www.zbmath.org/authors/?q=ai:hachicha.skanderDynamics of quantum correlations in a qubit-oscillator system interacting via a dissipative bath.https://www.zbmath.org/1453.810432021-02-27T13:50:00+00:00"Badveli, R."https://www.zbmath.org/authors/?q=ai:badveli.r"Jagadish, V."https://www.zbmath.org/authors/?q=ai:jagadish.vinayak"Akshaya, S."https://www.zbmath.org/authors/?q=ai:akshaya.s"Srikanth, R."https://www.zbmath.org/authors/?q=ai:srikanth.radhakrishnan|srikanth.raghavendran|srikanth.rajan"Petruccione, F."https://www.zbmath.org/authors/?q=ai:petruccione.francescoDirected-completeness of quantum statistical experiments in the randomization order.https://www.zbmath.org/1453.810042021-02-27T13:50:00+00:00"Kuramochi, Yui"https://www.zbmath.org/authors/?q=ai:kuramochi.yuiPure states of maximum uncertainty with respect to a given POVM.https://www.zbmath.org/1453.810032021-02-27T13:50:00+00:00"Szymusiak, Anna"https://www.zbmath.org/authors/?q=ai:szymusiak.annaDynamical semigroups in the Birkhoff polytope of order 3 as a tool for analysis of quantum channels.https://www.zbmath.org/1453.810092021-02-27T13:50:00+00:00"Snamina, Mateusz"https://www.zbmath.org/authors/?q=ai:snamina.mateusz"Zak, Emil J."https://www.zbmath.org/authors/?q=ai:zak.emil-jTwo-photon propagation of light and the modified Liouville equation.https://www.zbmath.org/1453.810662021-02-27T13:50:00+00:00"Kamchatnov, A. M."https://www.zbmath.org/authors/?q=ai:kamchatnov.anatoly-m"Pavlov, M. V."https://www.zbmath.org/authors/?q=ai:pavlov.maxim-vSummary: We show that the system of nonlinear equations of two-photon propagation of light with real amplitudes of the envelopes can be solved in general form by the classical Liouville method. This system, like other similar systems of Darboux-integrable equations, is related to the modified Liouville equation, and the found solution also provides general solutions of such modified equations. We conclude that the Liouville method provides an effective way to integrate a class of concrete system that admit Darboux integration.Deformation quantization of framed presymplectic manifolds.https://www.zbmath.org/1453.810422021-02-27T13:50:00+00:00"Gorev, N. D."https://www.zbmath.org/authors/?q=ai:gorev.n-d"Elfimov, B. M."https://www.zbmath.org/authors/?q=ai:elfimov.b-m"Sharapov, A. A."https://www.zbmath.org/authors/?q=ai:sharapov.adel-albertovich|sharapov.alexey-aSummary: We consider the problem of deformation quantization of presymplectic manifolds in the framework of the Fedosov method. A class of special presymplectic manifolds is distinguished for which such a quantization can always be constructed. We show that in the general case, the obstructions to quantization can be identified with some special elements of the third cohomology group of a differential ideal associated with the presymplectic structure.Quantum chosen-ciphertext attacks against Feistel ciphers.https://www.zbmath.org/1453.940912021-02-27T13:50:00+00:00"Ito, Gembu"https://www.zbmath.org/authors/?q=ai:ito.gembu"Hosoyamada, Akinori"https://www.zbmath.org/authors/?q=ai:hosoyamada.akinori"Matsumoto, Ryutaroh"https://www.zbmath.org/authors/?q=ai:matsumoto.ryutaroh"Sasaki, Yu"https://www.zbmath.org/authors/?q=ai:sasaki.yu"Iwata, Tetsu"https://www.zbmath.org/authors/?q=ai:iwata.tetsuSummary: Seminal results by \textit{M. Luby} and \textit{C. Rackoff} [SIAM J. Comput. 17, No. 2, 373--386 (1988; Zbl 0644.94018)] show that the 3-round Feistel cipher is secure against chosen-plaintext attacks (CPAs), and the 4-round version is secure against chosen-ciphertext attacks (CCAs). However, the security significantly changes when we consider attacks in the quantum setting, where the adversary can make superposition queries. By using Simon's algorithm that detects a secret cycle-period in polynomial-time, \textit{H. Kuwakado} and \textit{M. Morii} [Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: ISIT 2010, IEEE, 2682--2685 (2010)] showed that the 3-round version is insecure against quantum CPA by presenting a polynomial-time distinguisher. Since then, Simon's algorithm [\textit{D. R. Simon}, SIAM J. Comput. 26, No. 5, 1474--1483 (1997; Zbl 0883.03024)] has been heavily used against various symmetric-key constructions. However, its applications are still not fully explored.
In this paper, based on Simon's algorithm, we first formalize a sufficient condition of a quantum distinguisher against block ciphers so that it works even if there are multiple collisions other than the real period. This distinguisher is similar to the one proposed by \textit{T. Santoli} and \textit{C. Schaffner} [Using Simon's algorithm to attack symmetric-key cryptographic primitives. Quantum Inf. Comput. 17, No. 1-2, 65--78 (2017)], and it does not recover the period. Instead, we focus on the dimension of the space obtained from Simon's quantum circuit. This eliminates the need to evaluate the probability of collisions, which was needed in the work by \textit{M. Kaplan} et al. [Crypto 2016, Lect. Notes Comput. Sci. 9815, 207--237 (2016; Zbl 1391.94766)]. Based on this, we continue the investigation of the security of Feistel ciphers in the quantum setting. We show a quantum CCA distinguisher against the 4-round Feistel cipher. This extends the result of Kuwakado and Morii by one round, and follows the intuition of the result by Luby and Rackoff where the CCA setting can extend the number of rounds by one. We also consider more practical cases where the round functions are composed of a public function and XORing the subkeys. We show the results of both distinguishing and key recovery attacks against these constructions.
For the entire collection see [Zbl 1409.94003].Convergent perturbation theory for studying phase transitions.https://www.zbmath.org/1453.810492021-02-27T13:50:00+00:00"Nalimov, M. Yu."https://www.zbmath.org/authors/?q=ai:nalimov.m-yu"Ovsyannikov, A. V."https://www.zbmath.org/authors/?q=ai:ovsyannikov.a-vSummary: We propose a method for constructing a perturbation theory with a finite radius of convergence for a rather wide class of quantum field models traditionally used to describe critical and near-critical behavior in problems in statistical physics. For the proposed convergent series, we use an instanton analysis to find the radius of convergence and also indicate a strategy for calculating their coefficients based on the diagrams in the standard (divergent) perturbation theory. We test the approach in the example of the standard stochastic dynamics A-model and a matrix model of the phase transition in a system of nonrelativistic fermions, where its application allows explaining the previously observed quasiuniversal behavior of the trajectories of a first-order phase transition.Optimal time evolution for pseudo-Hermitian Hamiltonians.https://www.zbmath.org/1453.810212021-02-27T13:50:00+00:00"Wang, W. H."https://www.zbmath.org/authors/?q=ai:wang.wenhuan|wang.weihong|wang.weihan|wang.weihua.1|wang.wenhai|wang.weihua|wang.wenhu|wang.wen-hong|wang.wen-hung|wang.wenhe|wang.wanheng|wang.wei-hsiang|wang.wuhong|wang.weihui|wang.weihu|wang.wenhui|wang.wenhua|wang.wenhao"Chen, Z. L."https://www.zbmath.org/authors/?q=ai:chen.zeliang|chen.zhenlong|chen.zhonglian|chen.zili|chen.zhili|chen.zhao-li|chen.zhanglong|chen.zhonglin|chen.zenglu|chen.zhuliang|chen.zhaolin|chen.zhanglu|chen.zhongli|chen.zilin|chen.zhi-lai|chen.zhilan|chen.zilong|chen.zaoli|chen.zhilin|chen.zailiang|chen.zuo-li|chen.zhengli|chen.zhenlin|chen.zhong-liang|chen.zhi-long|chen.zhelin"Song, Y."https://www.zbmath.org/authors/?q=ai:song.yudan|song.yisheng|song.yingchun|song.yawei|song.yue|song.yinglei|song.yinqin|song.yuning|song.yuqin|song.yaxing|song.yirong|song.yuewu|song.yang|song.yongzhong|song.yongchen|song.yutao|song.yiliao|song.yuanmin|song.yisheng.1|song.yunpeng|song.yuzhao|song.yin|song.yongzhi|song.youjin|song.yuling|song.youngjin|song.yoonki|song.yanguo|song.yongduan|song.yingwei|song.yongdong|song.yinfang|song.yanbin|song.yueyue|song.ying|song.yongsoo|song.yuanfeng|song.yuhong|song.yukun|song.ya|song.yantao|song.yanyan|song.yumeng|song.yihong|song.yuming|song.yonghui|song.yuanzhuo|song.yaoyan|song.yanqi|song.yaqin|song.yu|song.yiwen|song.yalin|song.yueqiang|song.yuxia|song.yuhai|song.yongjin|song.yuanlong|song.yanzhi|song.yongji|song.yingxiang|song.yongjia|song.yufeng|song.you|song.yanan|song.yingliang|song.yongbo|song.yuyue|song.yongtao|song.yanglei|song.yanling|song.yating|song.yongcun|song.yamin|song.yinghui|song.yifan|song.yaozu|song.yurong|song.yongxin|song.yixian|song.yushu|song.yupeng|song.yuntao|song.yanli|song.yongkyu|song.yingda|song.yunxia|song.yinan|song.yooseob|song.yao|song.yuhe|song.yanhong|song.yuxiao|song.yueying|song.yuying|song.yunqiu|song.youngkwon|song.yuping|song.yafang|song.yanxing|song.yongli|song.yimei|song.yanxi|song.yangbo|song.yuting|song.yingwen|song.yuqing|song.yankui|song.yiwei|song.yi|song.yongpeng|song.yangqiu|song.yunhong|song.yun|song.yizhuang|song.yulong|song.yongsheng|song.yuqiao|song.youcheng|song.yazhi|song.yali|song.yeunjoo|song.yunyan|song.yanpo|song.yujian|song.yanjie|song.yingjie|song.yuanwei|song.yeongseok|song.yimin|song.yijun|song.yibing|song.yunfei|song.youngsun|song.yubo|song.yanlin|song.yongcheng|song.yuanping|song.yanqiu|song.yunsheng|song.yan|song.yexin|song.yongming|song.yaqian|song.yajun|song.yanli.1|song.yibin|song.yuanzhang|song.youngbae|song.yungwoo|song.yalong|song.yanlai|song.yonghong|song.yulin|song.yuanyuan|song.yujie|song.yunan|song.yanhua|song.yonghua|song.yuhua|song.yinglin|song.yafei|song.yujing|song.yong|song.yunkui|song.yingying|song.yifu|song.yupu|song.yihua|song.yunna|song.yunzhong|song.yuantao|song.yeqiong|song.yilin|song.yangwei|song.yixu|song.yingqing|song.yunquan|song.yonghyun|song.yuquan|song.yanping|song.yaru|song.yunchao|song.yingli"Fan, Y. J."https://www.zbmath.org/authors/?q=ai:fan.ya-ju|fan.yijun|fan.yuan-jia|fan.yijia|fan.yanjun|fan.yingjie|fan.yajing|fan.yu-jenSummary: If an initial state \(|\psi_{\mathrm{I}} \rangle\) and a final state \(|\psi_{\mathrm{F}} \rangle\) are given, then there exist many Hamiltonians under whose action \(|\psi_{\mathrm{I}}\rangle\) evolves into \(|\psi_{\mathrm{F}} \rangle \). In this case, the problem of the transition of \(|\psi_{\mathrm{I}} \rangle\) to \(|\psi_{\mathrm{F}} \rangle \) in the least time is very interesting. It was previously shown that for a Hermitian Hamiltonian, there is an optimum evolution time if \(|\psi_{\mathrm{I}} \rangle\) and \(|\psi_{\mathrm{F}} \rangle \) are orthogonal. But for a \(PT\)-symmetric Hamiltonian, this time can be arbitrarily small, which seems amazing. We discuss the optimum time evolution for pseudo-Hermitian Hamiltonians and obtain a lower bound for the evolution time under the condition that the Hamiltonian is bounded. The optimum evolution time can be attained in the case where two quantum states are orthogonal with respect to some inner product. The results in the Hermitian and pseudo-Hermitian cases coincide if the evolution is unitary with some well-defined inner product. We also analyze two previously studied examples and find that they are consistent with our theory. In addition, we give some explanations of our results with two examples.Airy functions and transition between semiclassical and harmonic oscillator approximations for one-dimensional bound states.https://www.zbmath.org/1453.810242021-02-27T13:50:00+00:00"Anikin, A. Yu."https://www.zbmath.org/authors/?q=ai:anikin.a-yu"Dobrokhotov, S. Yu."https://www.zbmath.org/authors/?q=ai:dobrokhotov.sergei-yu"Tsvetkova, A. V."https://www.zbmath.org/authors/?q=ai:tsvetkova.anna-vSummary: We consider the one-dimensional Schrödinger operator with a semiclassical small parameter \(h\). We show that the ``global'' asymptotic form of its bound states in terms of the Airy function ``works'' not only for excited states \(n\sim1/h\) but also for semi-excited states \(n\sim1/h^\alpha\), \(\alpha>0\), and, moreover, \(n\) starts at \(n=2\) or even \(n=1\) in examples. We also prove that the closeness of such an asymptotic form to the eigenfunction of the harmonic oscillator approximation.Atom scattering off a vibrating surface: an example of chaotic scattering with three degrees of freedom.https://www.zbmath.org/1453.370782021-02-27T13:50:00+00:00"Gonzalez Montoya, Francisco"https://www.zbmath.org/authors/?q=ai:gonzalez-montoya.francisco"Borondo, Florentino"https://www.zbmath.org/authors/?q=ai:borondo.florentino"Jung, Christof"https://www.zbmath.org/authors/?q=ai:jung.christofSummary: We study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degree of freedom (3-dof) model is studied by first considering the non-vibrating 2-dof model for different values of the energy. The set of singularities of the scattering functions shows the structure of the tangle between the stable and unstable manifolds of the fixed point at an infinite distance to the Cu surface in the Poincaré map. These invariant manifolds of the 2-dof system and their tangle can be used as a starting point for the construction of the stable and unstable manifolds and their tangle for the 3-dof coupled model. When the surface vibrates, the system has an extra closed degree of freedom and it is possible to represent the 3-dof tangle as deformation of a stack of 2-dof tangles, where the stack parameter is the energy of the 2-dof system. Also for the 3-dof system, the resulting invariant manifolds have the correct dimension to divide the constant total energy manifold. By this construction, it is possible to understand the chaotic scattering phenomena for the 3-dof system from a geometric point of view. We explain the connection between the set of singularities of the scattering function, the Jacobian determinant of the scattering function, the relevant invariant manifolds in the scattering problem, and the cross-section, as well as their behavior when the coupling due to the surface vibration is switched on. In particular, we present in detail the relation between the changes as a function of the energy in the structure of the caustics in the cross-section and the changes in the zero level set of the Jacobian determinant of the scattering function.On quantum slide attacks.https://www.zbmath.org/1453.940622021-02-27T13:50:00+00:00"Bonnetain, Xavier"https://www.zbmath.org/authors/?q=ai:bonnetain.xavier"Naya-Plasencia, María"https://www.zbmath.org/authors/?q=ai:naya-plasencia.maria"Schrottenloher, André"https://www.zbmath.org/authors/?q=ai:schrottenloher.andreSummary: At Crypto 2016, [Lect. Notes Comput. Sci. 9815, 207--237 (2016; Zbl 1391.94766)] \textit{M. Kaplan} et al. proposed the first quantum exponential acceleration of a classical symmetric cryptanalysis technique: they showed that, in the superposition query model, Simon's algorithm could be applied to accelerate the slide attack on the alternate-key cipher. This allows to recover an \(n\)-bit key with \(\mathcal{O}(n)\) queries.
In this paper we propose many other types of quantum slide attacks, inspired by classical techniques including sliding with a twist, complementation slide and mirror slidex. We also propose four-round self-similarity attacks for Feistel ciphers when using XOR operations. Some of these variants combined with whitening keys (FX construction) can also be successfully attacked. We present a surprising new result involving composition of quantum algorithms, that allows to combine some quantum slide attacks with a quantum attack on the round function, allowing an efficient key-recovery even if this function is strong classically.
Finally, we analyze the case of quantum slide attacks exploiting cycle-finding, whose possibility was mentioned in a paper by Bar-On et al. in 2015, where these attacks were introduced. We show that the speed-up is smaller than expected and less impressive than the above variants, but nevertheless provide improved complexities on the previous known quantum attacks in the superposition model for some self-similar SPN and Feistel constructions.
For the entire collection see [Zbl 1430.94005].On the geometry of magnetic skyrmions on thin films.https://www.zbmath.org/1453.820922021-02-27T13:50:00+00:00"Walton, Edward"https://www.zbmath.org/authors/?q=ai:walton.edwardSummary: We study the recently introduced `critically coupled' model of magnetic Skyrmions, generalising it to thin films with curved geometry. The model feels keenly the extrinsic geometry of the film in three-dimensional space. We find exact Skyrmion solutions on spherical, conical and cylindrical thin films. Axially symmetric solutions on cylindrical films are described by kinks tunnelling between `vacua'. For the model defined on general compact thin films, we prove the existence of energy minimising multi-Skyrmion solutions and construct the (resolved) moduli space of these solutions.Planar Ising model at criticality: state-of-the-art and perspectives.https://www.zbmath.org/1453.820062021-02-27T13:50:00+00:00"Chelkak, Dmitry"https://www.zbmath.org/authors/?q=ai:chelkak.dmitryCombinatorial Auslander-Reiten quivers and reduced expressions.https://www.zbmath.org/1453.160142021-02-27T13:50:00+00:00"Oh, Se-Jin"https://www.zbmath.org/authors/?q=ai:oh.se-jin"Suh, Uhi Rinn"https://www.zbmath.org/authors/?q=ai:suh.uhi-rinnSummary: In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes \([\widetilde{w}]\) of \(w\) in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order \(\prec_{[\widetilde{w}]}\) on the subset \(\Phi(w)\) of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class \([\widetilde{w}_0]\) of the longest element \(w_0\) of any finite type.Correction to: The standard model in noncommutative geometry: fundamental fermions as internal forms.https://www.zbmath.org/1453.580032021-02-27T13:50:00+00:00"Dąbrowski, Ludwik"https://www.zbmath.org/authors/?q=ai:dabrowski.ludwik"D'Andrea, Francesco"https://www.zbmath.org/authors/?q=ai:dandrea.francesco"Sitarz, Andrzej"https://www.zbmath.org/authors/?q=ai:sitarz.andrzejSummary: Corrects a grant number in the authors's paper [ibid. 108, No. 5, 1323--1340 (2018; Zbl 1395.58007)].Reply to ``Comment on: `Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in a rotating frame'''.https://www.zbmath.org/1453.810152021-02-27T13:50:00+00:00"Hassanabadi, H."https://www.zbmath.org/authors/?q=ai:hassanabadi.hassan"Hosseinpour, M."https://www.zbmath.org/authors/?q=ai:hosseinpour.mansoureh"de Montigny, M."https://www.zbmath.org/authors/?q=ai:de-montigny.marcFrom the text: This reply concers the comment by \textit{Francisco M. Fernández} [ibid. 419, Article ID 168243, 3 p. (2020; Zbl 1448.81305)]. In response to the last paragraph of the comment, the Heun equation, which the authors reached in Eq. (23) of their paper can be solved by the Ansatz method, the Quasi-Exact-Solvable method and the Frobenius method. The authors have used the well-known Frobenius method; the Heun equation is utilized in many papers which apply the same method, and in most of them, the same two conditions as appear in our paper, that is, \(C - a - 2 = 2n_0,\, C_{n_0+2} = 0.\)
Therefore the results of our paper are correct and the comment is unnecassary.The quantum universe. Essays on quantum mechanics, quantum cosmology, and physics in general.https://www.zbmath.org/1453.810012021-02-27T13:50:00+00:00"Hartle, James B."https://www.zbmath.org/authors/?q=ai:hartle.james-bPublisher's description: As physics has progressed, its most fundamental theories have become more distant from everyday experience posing challenges for understanding, notably with quantum mechanics. This volume contains twenty-nine essays written to address such challenges. The essays address issues in quantum mechanics, quantum cosmology and physics in general. Examples include: How do we apply quantum mechanics to the whole universe when all observers are inside? What do we mean by past, present, and future in a four-dimensional universe? What is the origin of classical predictability in a quantum universe? Could physics predict non-computable numbers? Short personal recollections of Murray Gell-Mann and Stephen Hawking are included.
The essays vary in length, style, and level but should be accessible to most physicists.An algebraic geometric classification of superintegrable systems in the Euclidean plane.https://www.zbmath.org/1453.370582021-02-27T13:50:00+00:00"Kress, Jonathan"https://www.zbmath.org/authors/?q=ai:kress.jonathan-m"Schöbel, Konrad"https://www.zbmath.org/authors/?q=ai:schobel.konrad-pSummary: We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by deriving an explicit system of homogeneous algebraic equations. We then solve these equations and give a detailed analysis of the algebraic geometric structure of the corresponding projective variety. This naturally associates a unique planar line triple arrangement to every superintegrable system, providing a geometric realisation of this variety and an intrinsic labelling scheme. In particular, our results confirm the known classification by independent, purely algebraic means.The algebra of Wick polynomials of a scalar field on a Riemannian manifold.https://www.zbmath.org/1453.810502021-02-27T13:50:00+00:00"Dappiaggi, Claudio"https://www.zbmath.org/authors/?q=ai:dappiaggi.claudio"Drago, Nicolò"https://www.zbmath.org/authors/?q=ai:drago.nicolo"Rinaldi, Paolo"https://www.zbmath.org/authors/?q=ai:rinaldi.paoloSpectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation.https://www.zbmath.org/1453.810262021-02-27T13:50:00+00:00"Ibrogimov, Orif O."https://www.zbmath.org/authors/?q=ai:ibrogimov.orif-oChirality induced interface currents in the Chalker-Coddington model.https://www.zbmath.org/1453.820312021-02-27T13:50:00+00:00"Asch, Joachim"https://www.zbmath.org/authors/?q=ai:asch.joachim"Bourget, Olivier"https://www.zbmath.org/authors/?q=ai:bourget.olivier"Joye, Alain"https://www.zbmath.org/authors/?q=ai:joye.alainSummary: We study transport properties of a Chalker-Coddington type model in the plane which presents asymptotically pure anti-clockwise rotation on the left and clockwise rotation on the right. We prove delocalisation in the sense that the absolutely continuous spectrum covers the whole unit circle. The result is of topological nature and independent of the details of the model.Factors generated by \textit{XY}-model with competing Ising interactions on the Cayley tree.https://www.zbmath.org/1453.460572021-02-27T13:50:00+00:00"Mukhamedov, Farrukh"https://www.zbmath.org/authors/?q=ai:mukhamedov.farruh-m"El Gheteb, Soueidy"https://www.zbmath.org/authors/?q=ai:el-gheteb.soueidyAuthors' abstract: In the present paper, we consider a quantum Markov chain corresponding to the \textit{XY}-model with competing Ising interactions on the Cayley tree of order two. Earlier, it was proved that this state does exist and is unique. Moreover, it has clustering property. This means that the von Neumann algebra generated by this state is a factor. In the present paper, we establish that the factor generated by this state may have type \(\text{III}_{\lambda }$, $ \lambda \in (0,1)\), which is unusual for states associated with models with nontrivial interactions.
Reviewer: Nasir N. Ganikhodjaev (Tashkent)On various functional representations of the space of Schwartz operators.https://www.zbmath.org/1453.810052021-02-27T13:50:00+00:00"Amosov, G. G."https://www.zbmath.org/authors/?q=ai:amosov.grigori-gSummary: In this paper, we discuss various representations in which the space \(S\) of Schwartz operators turns into the space of test functions, whereas the dual space \(S'\) turns into the space of generalized functions.Spinor-helicity formalism for massless fields in \(\mathrm{AdS}_4\). II: Potentials.https://www.zbmath.org/1453.810542021-02-27T13:50:00+00:00"Nagaraj, Balakrishnan"https://www.zbmath.org/authors/?q=ai:nagaraj.balakrishnan"Ponomarev, Dmitry"https://www.zbmath.org/authors/?q=ai:ponomarev.dmitry-m|ponomarev.dmitry-vSummary: In a recent letter we suggested a natural generalization of the flat-space spinor-helicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane-wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism.Strange duality revisited.https://www.zbmath.org/1453.810552021-02-27T13:50:00+00:00"Pauly, Christian"https://www.zbmath.org/authors/?q=ai:pauly.christianSummary: We give a proof of the strange duality or rank-level duality of the WZW models of conformal blocks by extending the genus-\(0\) result, obtained by \textit{T. Nakanishi} and \textit{A. Tsuchiya} [Commun. Math. Phys. 144, No. 2, 351--372 (1992; Zbl 0751.17024)], to higher genus curves via the sewing procedure. The new ingredient of the proof is an explicit use of the branching rules of the conformal embedding of affine Lie algebras \(\widehat{\mathfrak{sl}(r)} \times \widehat{\mathfrak{sl}(l)} \subset \widehat{\mathfrak{sl}(rl)}\). We recover the strange duality of spaces of generalized theta functions obtained by Belkale, Marian-Oprea, as well as by Oudompheng in the parabolic case.On \(\mathbb{Z}_2\)-indices for ground states of fermionic chains.https://www.zbmath.org/1453.810572021-02-27T13:50:00+00:00"Bourne, Chris"https://www.zbmath.org/authors/?q=ai:bourne.chris"Schulz-Baldes, Hermann"https://www.zbmath.org/authors/?q=ai:schulz-baldes.hermannGlobal multiplicity bounds and spectral statistics for random operators.https://www.zbmath.org/1453.810272021-02-27T13:50:00+00:00"Mallick, Anish"https://www.zbmath.org/authors/?q=ai:mallick.anish"Maddaly, Krishna"https://www.zbmath.org/authors/?q=ai:maddaly.krishnaIntroduction to the BV-BFV formalism.https://www.zbmath.org/1453.810562021-02-27T13:50:00+00:00"Cattaneo, Alberto S."https://www.zbmath.org/authors/?q=ai:cattaneo.alberto-sergio"Moshayedi, Nima"https://www.zbmath.org/authors/?q=ai:moshayedi.nimaCanonical quantization of constants of motion.https://www.zbmath.org/1453.810412021-02-27T13:50:00+00:00"Belmonte, Fabián"https://www.zbmath.org/authors/?q=ai:belmonte.fabianScattering of particles bounded to an infinite planar curve.https://www.zbmath.org/1453.810252021-02-27T13:50:00+00:00"Dittrich, J."https://www.zbmath.org/authors/?q=ai:dittrich.jaroslav|dittrich.jens|dittrich.jorg-sQuantum line defects and refined BPS spectra.https://www.zbmath.org/1453.141322021-02-27T13:50:00+00:00"Cirafici, Michele"https://www.zbmath.org/authors/?q=ai:cirafici.micheleSummary: In this note, we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class \(\mathcal{S}\). Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR, they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the \(K\)-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular, refined framed BPS states are described via Euler characteristics of certain complexes of sheaves.A research on defect image enhancement based on partial differential equation of quantum mechanics.https://www.zbmath.org/1453.940212021-02-27T13:50:00+00:00"Wang, Zhonghua"https://www.zbmath.org/authors/?q=ai:wang.zhonghua"Wang, Feiwen"https://www.zbmath.org/authors/?q=ai:wang.feiwen"Chi, Guiying"https://www.zbmath.org/authors/?q=ai:chi.guiyingSummary: The defect image enhancement of aeronautic component is vital for the defect quantitative and qualitative properties. In this paper, a novel defect image enhancement algorithm is presented, which adopts the partial differential equation of quantum mechanics. The algorithm includes two key steps as follows. Firstly, according to the quantum mechanics theory, the image edge quantum probability is computed. Secondly, the partial differential equation coupling the anisotropic edge quantum probability is constructed to enhance the defect images of aeronautical component. Compared with other methods, the experimental results indicate that the proposed method better highlight the defect images.Symmetry breaking. 3rd edition.https://www.zbmath.org/1453.810382021-02-27T13:50:00+00:00"Strocchi, Franco"https://www.zbmath.org/authors/?q=ai:strocchi.francoPublisher's description: The third edition of the by now classic reference on rigorous analysis of symmetry breaking in both classical and quantum field theories adds new topics of relevance, in particular the effect of dynamical Coulomb delocalization, by which boundary conditions give rise to volume effects and to energy/mass gap in the Goldstone spectrum (plasmon spectrum, Anderson superconductivity, Higgs phenomenon). The book closes with a discussion of the physical meaning of global and local gauge symmetries and their breaking, with attention to the effect of gauge group topology in QCD.
See the reviews of the first and second editions in [Zbl 1075.81003; Zbl 1145.81037].Equivariant higher Hochschild homology and topological field theories.https://www.zbmath.org/1453.570252021-02-27T13:50:00+00:00"Müller, Lukas"https://www.zbmath.org/authors/?q=ai:muller.lukas"Woike, Lukas"https://www.zbmath.org/authors/?q=ai:woike.lukasSummary: We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group \(G\). As coefficients, we allow \(E_{\infty}\)-algebras with \(G\)-action. For this homology theory, we establish an equivariant version of excision and prove that it extends to an equivariant topological field theory with values in the \((\infty , 1)\)-category of cospans of \(E_{\infty}\)-algebras.Chiral properties of discrete Joyce and Hestenes equations.https://www.zbmath.org/1453.810192021-02-27T13:50:00+00:00"Sushch, Volodymyr"https://www.zbmath.org/authors/?q=ai:sushch.volodymyrSummary: This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-Kähler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be described with the aid of some projectors on a space of discrete forms. The proposed discrete model admits a chiral symmetry. We construct discrete analogues of spin operators, describe spin eigenstates for a discrete Joyce equation, and also discuss chirality.
For the entire collection see [Zbl 1445.34003].On braided, banded surfaces and ribbon obstructions.https://www.zbmath.org/1453.570042021-02-27T13:50:00+00:00"Grigsby, J. Elisenda"https://www.zbmath.org/authors/?q=ai:grigsby.julia-elisendaSummary: We discuss how to apply work of L. Rudolph to braid conjugacy class invariants to obtain potentially effective obstructions to a slice knot being ribbon. We then apply these ideas to a family of braid conjugacy class invariants [\textit{J. E. Grigsby} et al., Pure Appl. Math. Q. 13, No. 3, 389--436 (2018; Zbl 1411.57013)] coming from Khovanov-Lee theory and explain why we do not obtain effective ribbon obstructions in this case.
For the entire collection see [Zbl 1420.00044].Self-localized solitons of a \(q\)-deformed quantum system.https://www.zbmath.org/1453.351602021-02-27T13:50:00+00:00"Bayındır, Cihan"https://www.zbmath.org/authors/?q=ai:bayindir.cihan"Altintas, Azmi Ali"https://www.zbmath.org/authors/?q=ai:altintas.azmi-ali"Ozaydin, Fatih"https://www.zbmath.org/authors/?q=ai:ozaydin.fatihSummary: Beyond a pure mathematical interest, \(q\)-deformation is promising for the modeling and interpretation of various physical phenomena. In this paper, we numerically investigate the existence and properties of the self-localized soliton solutions of the nonlinear Schrödinger equation (NLSE) with a \(q\)-deformed Rosen-Morse potential. By implementing a Petviashvili method (PM), we obtain the self-localized one and two soliton solutions of the NLSE with a \(q\)-deformed Rosen-Morse potential. In order to investigate the temporal behavior and stabilities of these solitons, we implement a Fourier spectral method with a 4th order Runge-Kutta time integrator. We observe that the self-localized one and two solitons are stable and remain bounded with a pulsating behavior and minor changes in the sidelobes of the soliton waveform. Additionally, we investigate the stability and robustness of these solitons under noisy perturbations. A sinusoidal monochromatic wave field modeled within the frame of the NLSE with a \(q\)-deformed Rosen-Morse potential turns into a chaotic wavefield and exhibits rogue oscillations due to modulation instability triggered by noise, however, the self-localized solitons of the NLSE with a \(q\)-deformed Rosen-Morse potential are stable and robust under the effect of noise. We also show that soliton profiles can be reconstructed after a denoising process performed using a Savitzky-Golay filter.Symbolic algorithm for generating irreducible rotational-vibrational bases of point groups.https://www.zbmath.org/1453.200022021-02-27T13:50:00+00:00"Gusev, A. A."https://www.zbmath.org/authors/?q=ai:gusev.alexander-a"Gerdt, V. P."https://www.zbmath.org/authors/?q=ai:gerdt.vladimir-p"Vinitsky, S. I."https://www.zbmath.org/authors/?q=ai:vinitsky.sergue-i"Derbov, V. L."https://www.zbmath.org/authors/?q=ai:derbov.vladimir-l"Góźdź, A."https://www.zbmath.org/authors/?q=ai:gozdz.andrzej"Pȩdrak, A."https://www.zbmath.org/authors/?q=ai:pedrak.a"Szulerecka, A."https://www.zbmath.org/authors/?q=ai:szulerecka.a"Dobrowolski, A."https://www.zbmath.org/authors/?q=ai:dobrowolski.arkadiuszSummary: Symbolic algorithm implemented in computer algebra system for generating irreducible representations of the point symmetry groups in the rotor + shape vibrational space of a nuclear collective model in the intrinsic frame is presented. The method of generalized projection operators is used. The generalized projection operators for the intrinsic group acting in the space \(\mathrm {L}^2(\mathrm{SO(3)})\) and in the space spanned by the eigenfunctions of a multidimensional harmonic oscillator are constructed. The efficiency of the scheme is investigated by calculating the bases of irreducible representations subgroup \(\overline{\mathrm{D}}_{4y}\) of octahedral group in the intrinsic frame of a quadrupole-octupole nuclear collective model.
For the entire collection see [Zbl 1346.68010].High order efficient splittings for the semiclassical time-dependent Schrödinger equation.https://www.zbmath.org/1453.810302021-02-27T13:50:00+00:00"Blanes, Sergio"https://www.zbmath.org/authors/?q=ai:blanes.sergio"Gradinaru, Vasile"https://www.zbmath.org/authors/?q=ai:gradinaru.vasileSummary: Standard numerical schemes with time-step \(h\) deteriorate (e.g. like \(\varepsilon^{-2}h^2)\) in the presence of a small semiclassical parameter \(\epsilon\) in the time-dependent Schrödinger equation. The recently introduced semiclassical splitting was shown to be of order \(\mathcal{O}(\varepsilon h^2)\). We present now an algorithm that is of order \(\mathcal{O}(\varepsilon h^7+\varepsilon^2 h^6+\varepsilon^3h^4)\) at the expense of roughly three times the computational effort of the semiclassical splitting and another that is of order \(\mathcal{O}(\varepsilon h^6+\varepsilon^2h^4)\) at the \textit{same} expense of the computational effort of the semiclassical splitting.One-dimensional localized modes of spin-orbit-coupled Bose-Einstein condensates with spatially periodic modulated atom-atom interactions: nonlinear lattices.https://www.zbmath.org/1453.820422021-02-27T13:50:00+00:00"Chen, Junbo"https://www.zbmath.org/authors/?q=ai:chen.junbo"Zeng, Jianhua"https://www.zbmath.org/authors/?q=ai:zeng.jianhuaSummary: Bose-Einstein condensates (BECs) provide a clear and controllable platform to study diverse intriguing emergent nonlinear effects that appear too in other physical settings, such as bright and dark solitons in mean-field theory as well as many-body physics. Various ways have been elaborated to stabilize bright solitons in BECs, three promising schemes among which are: optical lattices formed by counterpropagating laser beams, nonlinear managements mediated by Feshbach resonance, spin-orbit coupling engineered by dressing atomic spin states (hyperfine states of spinor atomic BECs) with laser beams. By combing the latter two schemes, we discover, from theory to calculations, that the two-component BECs with a spin-orbit coupling and cubic atom-atom interactions, whose nonlinear distributions exhibit a well-defined spatially periodic modulation (nonlinear lattice), can support one-dimensional localized modes of two kinds: fundamental solitons (with a single peak), and soliton pairs comprised of dipole solitons (anti-phase) or two-peak solitons (in-phase). The influence of three physical parameters: chemical potential of the system, strengths of both the Rashba spin-orbit coupling and atom-atom interactions, on the existence and stability of the localized modes is investigated based on linear-stability analysis and direct perturbed simulations. In particular, we demonstrate that the localized modes can be stable objects provided always that both the inter- and intraspecies interactions are attractive.Discrete symmetries of complete intersection Calabi-Yau manifolds.https://www.zbmath.org/1453.141092021-02-27T13:50:00+00:00"Lukas, Andre"https://www.zbmath.org/authors/?q=ai:lukas.andre"Mishra, Challenger"https://www.zbmath.org/authors/?q=ai:mishra.challengerSummary: In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi-Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi-Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of complete intersection manifolds by freely-acting discrete symmetries, non-freely-acting, generic symmetries arise in 381 cases and are, therefore, a relatively common feature of these manifolds. We find that 9 different discrete groups appear, ranging in group order from 2 to 18, and that both regular symmetries and R-symmetries are possible.\(\mathrm{E}_8\) spectral curves.https://www.zbmath.org/1453.140892021-02-27T13:50:00+00:00"Brini, Andrea"https://www.zbmath.org/authors/?q=ai:brini.andreaThe aim of this paper is to provide an explicit construction of
spectral curves for the affine \(E_8\) relativistic Toda chain.
Their closed form expression is obtained by determining the full
set of character relations in the representation ring of \(E_8\) for
the exterior algebra of the adjoint representation; this is in
turn employed to provide an explicit construction of both
integrals of motion and the action-angle map for the resulting
integrable system. The author considers two main areas of
applications of these constructions. On the one hand, he considers
the resulting family of spectral curves in the context of the
correspondences between Toda systems, five-dimensional
Seiberg-Witten theory, Gromov-Witten theory of orbifolds of the
resolved conifold, and Chern-Simons theory to establish a version
of the B-model Gopakumar-Vafa correspondence for the \(sl_N\)
Lê-Murakami-Ohtsuki invariant of the Poincaré integral
homology sphere to all orders in \(1/N\). On the other, the author
considers a degenerate version of the spectral curves and proves a
one-dimensional Landau-Ginzburg mirror theorem for the Frobenius
manifold structure on the space of orbits of the extended affine
Weyl group of type \(E_8\) introduced by Dubrovin-Zhang
(equivalently, the orbifold quantum cohomology of the type-\(E_8\)
polynomial \(CP^1\) orbifold). This leads to closed-form expressions
for the flat co-ordinates of the Saito metric, the prepotential,
and a higher genus mirror theorem based on the
Chekhov-Eynard-Orantin recursion. The author also shows how the
constructions of the paper lead to a generalisation of a
conjecture of Norbury-Scott to ADE \(\mathbb{P}^1\)-orbifolds, and a
mirror of the Dubrovin-Zhang construction for all Weyl groups and
choices of marked roots. Some facets of the problems addressed in
this paper have surfaced with a different angle in previous works
in the literature, and in order to make the text self-contained
the author reviews as necessary the links with their methodology
at the beginning of each Section. This paper is organized as
follows : the first section is an introduction to the subject and
a description of the results. Section 2, deals with the \(E_8\) and
\(\widehat{E_8}\) relativistic Toda chain and Section 3, with
action-angle variables and the preferred Prym-Tyurin. Sections 4
and 5 deals with applications. Application I: gauge theory and
Toda and Application II: the \(\widehat{E_8}\) Frobenius. The paper
is supported with some appendices.
Reviewer: Ahmed Lesfari (El Jadida)Hall effects on hydromagnetic natural convection flow in a vertical micro-porous-channel with injection/suction.https://www.zbmath.org/1453.850032021-02-27T13:50:00+00:00"Bhaskar, P."https://www.zbmath.org/authors/?q=ai:bhaskar.p"Venkateswarlu, M."https://www.zbmath.org/authors/?q=ai:venkateswarlu.m.1Summary: In this work, the hydromagnetic and thermal characteristics of natural convection flow in a vertical parallel plate micro-porous-channel with suction/injection is analytically studied in the presence of Hall current by taking the temperature jump and the velocity slip at the wall into account. The governing equations, exhibiting the physics of the flow formation are displayed and the exact analytical solutions have been obtained for momentum and energy equations under relevant boundary conditions. The impact of distinct admissible parameters such as Hartmann number, Hall current parameter, permeability parameter, suction/injection parameter, fluid wall interaction parameter, Knudsen number and wall-ambient temperature ratio on the flow formation is discussed with the aid of line graphs. In particular, as rarefaction parameter on the micro-porous-channel surfaces increases, the fluid velocity increases and the volume flow rate decreases for injection/suction.Optimal error estimate of a decoupled conservative local discontinuous Galerkin method for the Klein-Gordon-Schrödinger equations.https://www.zbmath.org/1453.652832021-02-27T13:50:00+00:00"Yang, He"https://www.zbmath.org/authors/?q=ai:yang.heSummary: In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.Quantum homomorphic encryption scheme with flexible number of evaluator based on \((k, n)\)-threshold quantum state sharing.https://www.zbmath.org/1453.810132021-02-27T13:50:00+00:00"Chen, Xiu-Bo"https://www.zbmath.org/authors/?q=ai:chen.xiu-bo"Sun, Yi-Ru"https://www.zbmath.org/authors/?q=ai:sun.yi-ru"Xu, Gang"https://www.zbmath.org/authors/?q=ai:xu.gang"Yang, Yi-Xian"https://www.zbmath.org/authors/?q=ai:yang.yi-xian|yang.yixianSummary: Quantum homomorphic encryption provides the ability to perform calculations on encrypted data without decrypting them. The number of evaluators in most previous schemes is 1, and in other schemes it is \(n\). In this paper, we propose a novel quantum homomorphic encryption scheme with flexible number of evaluator. One of our main contributions is that the number of evaluators is \(d\) (\(k \leq d \leq n\)), here \(n \geq 2\). These evaluators are allowed to alternately complete the evaluation of single-qubit unitary operations on the shared encrypted sequence. Other work is that for \(n = 1\), we also give the quantum homomorphic encryption scheme that one evaluator can complete the evaluation. Then, for \((3, 5)\)-case and \((2, 2)\)-case, we give two examples (i.e. example-I and example-II) to illustrate the flexibility of evaluators. Finally, it is shown that the scheme is secure from analyzing the private key, plaintext sequence and encrypted sequence.Quantum stream ciphers: impossibility of unconditionally strong algorithms.https://www.zbmath.org/1453.810142021-02-27T13:50:00+00:00"Tregubov, P. A."https://www.zbmath.org/authors/?q=ai:tregubov.p-a"Trushechkin, A. S."https://www.zbmath.org/authors/?q=ai:trushechkin.anton-sergeevichSummary: Stream ciphers form one of two large classes of ciphers with private keys in classical cryptography. In this paper, we introduce the concept of a quantum stream cipher. Special types of quantum stream ciphers were proposed earlier by numerous researchers. We prove a general result on the nonexistence of an unconditionally strong quantum stream cipher if the length of a message is much longer than the length of a key. We analyze individual and collective attacks against a quantum stream cipher. A relationship between the problem of guessing the key by the opponent and the problem of distinguishing of random quantum states is established.Certain methods of constructing controls for quantum systems.https://www.zbmath.org/1453.810342021-02-27T13:50:00+00:00"Pechen', A. N."https://www.zbmath.org/authors/?q=ai:pechen.aleksandr-nikolaevich|pechen.alexander-nikolaevichSummary: Recently, various control problems for quantum systems, such as individual atoms, molecules, and electron states at quantum points, have been actively researched. In this paper, we briefly discuss methods of constructing controls for quantum system by means of gradient algorithms, genetic algorithms, and the speed gradient. The violation of the asymptotic stabilizability condition for the problem of generation of unitary operations is proved by the speed gradient method in two-level quantum systems.Asymmetry of locally available and locally transmitted information in thermal two-qubit states.https://www.zbmath.org/1453.810072021-02-27T13:50:00+00:00"Kiktenko, E. O."https://www.zbmath.org/authors/?q=ai:kiktenko.evgeniy-oSummary: In the paper, we consider thermal states of two particles with spin 1/2 (qubits) located in an inhomogeneous transverse magnetic field and interacting according to the Heisenberg \(XY\)-model. We introduce the concepts of magnitude and direction of asymmetry of the entropy of a state and the magnitude and asymmetry of a flow of locally transmitted information. We show that for the system considered, the asymmetry of entropy is directed from the particle in a weaker magnetic field toward the particle in a stronger magnetic field, and this direction coincides with the direction of the excess flow of locally transmitted information. We also demonstrate that this asymmetry direction is consistent with the direction of the excess flow of locally available information: measurements over the particle in a weaker magnetic field provide a greater level of locally available information than measurements over the particle in a stronger magnetic field.Quantum codes from the cyclic codes over \(\mathbb{F}_p[v,w]/\langle v^2-1,w^2-1,vw-wv\rangle\).https://www.zbmath.org/1453.810122021-02-27T13:50:00+00:00"Islam, Habibul"https://www.zbmath.org/authors/?q=ai:islam.habibul"Prakash, Om"https://www.zbmath.org/authors/?q=ai:prakash.om"Verma, Ram Krishna"https://www.zbmath.org/authors/?q=ai:verma.ram-krishnaSummary: In this article, for any odd prime \(p\), we study the cyclic codes over the finite ring \(R=\mathbb{F}_p[v,w]/\langle v^2-1,w^2-1,vw-wv\rangle\) to obtain the quantum codes over \(\mathbb{F}_p\). We obtain the necessary and sufficient condition for cyclic codes which contain their duals and as an application, some new quantum codes are presented at the end of the article.
For the entire collection see [Zbl 1443.00026].Fixed angle inverse scattering for almost symmetric or controlled perturbations.https://www.zbmath.org/1453.351932021-02-27T13:50:00+00:00"Rakesh"https://www.zbmath.org/authors/?q=ai:rakesh.shanti-lal|rakesh.nitin|rakesh.leela|rakesh.|rakesh.kumar|rakesh.s-g"Salo, Mikko"https://www.zbmath.org/authors/?q=ai:salo.mikkoGeneric asymptotics of resonance counting function for Schrödinger point interactions.https://www.zbmath.org/1453.350572021-02-27T13:50:00+00:00"Albeverio, Sergio"https://www.zbmath.org/authors/?q=ai:albeverio.sergio-a"Karabash, Illya M."https://www.zbmath.org/authors/?q=ai:karabash.illya-mUnder consideration are the Schrödinger Hamiltonians \(H_{a,y}\) with point interactions
\[
-\Delta u(x)+\sum_{i=1}^{N} \mu(a_{j})\delta(x-y_{j})u(x),\ \ x\in {\mathbb R}^{3}.
\]
The main result is that the resonance counting function for the operator \(H_{a,y}\) for a dense set of parameters \(\vec{a}\) has the Weyl-type asymptotics \(N_{H_{a,y}}=\frac{V(y)}{\pi}R+O(1)\), with \(V(y)=\max_{\sigma}\sum_{j=1}^{N}|y_{j}-y_{\sigma(j)}|\) where the maximium is taken over all permutations \(\sigma\).
For the entire collection see [Zbl 1445.00025].
Reviewer: Sergey G. Pyatkov (Khanty-Mansiysk)Weak limit theorem of a two-phase quantum walk with one defect.https://www.zbmath.org/1453.624062021-02-27T13:50:00+00:00"Endo, Shimpei"https://www.zbmath.org/authors/?q=ai:endo.shimpei"Endo, Takako"https://www.zbmath.org/authors/?q=ai:endo.takako"Konno, Norio"https://www.zbmath.org/authors/?q=ai:konno.norio"Segawa, Etsuo"https://www.zbmath.org/authors/?q=ai:segawa.etsuo"Takei, Masato"https://www.zbmath.org/authors/?q=ai:takei.masatoSummary: We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW ``the two-phase QW with one defect'', which we treated concerning localization theorems. The two-phase QW with one defect has been expected to be a mathematical model of topological insulator which is an intense issue both theoretically and experimentally. In this paper, we derive the weak limit theorem describing the ballistic spreading, and as a result, we obtain the mathematical expression of the whole picture of the asymptotic behavior. Our approach is based mainly on the generating function of the weight of the passages. We emphasize that the time-averaged limit measure is symmetric for the origin, however, the weak limit measure is asymmetric, which implies that the weak limit theorem represents the asymmetry of the probability distribution.Analysis in noncommutative algebras and modules.https://www.zbmath.org/1453.160302021-02-27T13:50:00+00:00"Zharinov, V. V."https://www.zbmath.org/authors/?q=ai:zharinov.victor-vSummary: In a previous paper [ibid. 301, 98--108 (2018; Zbl 1448.16038); translation from Tr. Mat. Inst. Steklova 301, 108--118 (2018)], we developed an analysis in associative commutative algebras and in modules over them, which may be useful in problems of contemporary mathematical and theoretical physics. Here we work out similar methods in the noncommutative case.Semiclassical asymptotics of the spectrum of the hydrogen atom in an electromagnetic field near the upper boundaries of spectral clusters.https://www.zbmath.org/1453.810632021-02-27T13:50:00+00:00"Migaeva, A. S."https://www.zbmath.org/authors/?q=ai:migaeva.a-s"Pereskokov, A. V."https://www.zbmath.org/authors/?q=ai:pereskokov.a-vSummary: We study the Zeeman-Stark effect in the hydrogen atom located in an electromagnetic field by using irreducible representations of an algebra with the Karasev-Novikova quadratic commutation relations. The representations are associated with resonance spectral clusters near the energy level of the unperturbed hydrogen atom. We find asymptotics for a series of eigenvalues and corresponding asymptotic eigenfunctions near the upper boundaries of spectral clusters in the case of positive intensities of the electric field.Quantum decomposition associated with the \(q\)-deformed Lévy-Meixner white noise.https://www.zbmath.org/1453.810332021-02-27T13:50:00+00:00"Riahi, Anis"https://www.zbmath.org/authors/?q=ai:riahi.anis"Ettaieb, Amine"https://www.zbmath.org/authors/?q=ai:ettaieb.amineA refined speed limit for the imaginary-time Schrödinger equation.https://www.zbmath.org/1453.810102021-02-27T13:50:00+00:00"Sun, Jie"https://www.zbmath.org/authors/?q=ai:sun.jie.2"Lu, Songfeng"https://www.zbmath.org/authors/?q=ai:lu.songfengQuantum error correction in the presence of initial system-environment correlations.https://www.zbmath.org/1453.810082021-02-27T13:50:00+00:00"Türkmen, A."https://www.zbmath.org/authors/?q=ai:turkmen.asuman-s|turkmen.ali-caner"Verçin, A."https://www.zbmath.org/authors/?q=ai:vercin.abdullahRényi entropy and Rényi divergence in sequential effect algebra.https://www.zbmath.org/1453.810022021-02-27T13:50:00+00:00"Giski, Zahra Eslami"https://www.zbmath.org/authors/?q=ai:eslami-giski.zahraDynamic correlations in open quantum systems: the dephasing model.https://www.zbmath.org/1453.810442021-02-27T13:50:00+00:00"Ignatyuk, Vasyl'"https://www.zbmath.org/authors/?q=ai:ignatyuk.vasylFew remarks on quasi quantum quadratic operators on \(\mathbb{M}_2(\mathbb{C})\).https://www.zbmath.org/1453.810282021-02-27T13:50:00+00:00"Mukhamedov, Farrukh"https://www.zbmath.org/authors/?q=ai:mukhamedov.farruh-m"Syam, Sondos M."https://www.zbmath.org/authors/?q=ai:syam.sondos-m"Almazrouei, Shamma A. Y."https://www.zbmath.org/authors/?q=ai:almazrouei.shamma-a-yNumerical methods for Bogoliubov-de Gennes excitations of Bose-Einstein condensates.https://www.zbmath.org/1453.810652021-02-27T13:50:00+00:00"Gao, Yali"https://www.zbmath.org/authors/?q=ai:gao.yali"Cai, Yongyong"https://www.zbmath.org/authors/?q=ai:cai.yongyongSummary: In this paper, we study the analytical properties and the numerical methods for the Bogoliubov-de Gennes equations (BdGEs) describing the elementary excitation of Bose-Einstein condensates around the mean field ground state, which is governed by the Gross-Pitaevskii equation (GPE). Derived analytical properties of BdGEs can serve as benchmark tests for numerical algorithms and three numerical methods are proposed to solve the BdGEs, including sine-spectral method, central finite difference method and compact finite difference method. Extensive numerical tests are provided to validate the algorithms and confirm that the sine-spectral method has spectral accuracy in spatial discretization, while the central finite difference method and the compact finite difference method are second-order and fourth-order accurate, respectively. Finally, sine-spectral method is extended to study elementary excitations under the optical lattice potential and solve the BdGEs around the first excited states of the GPE. The numerical experiments demonstrate the efficiency and accuracy of the proposed methods for solving BdGEs.Quantum mechanics of stationary states of particles in a space-time of classical black holes.https://www.zbmath.org/1453.810322021-02-27T13:50:00+00:00"Gorbatenko, M. V."https://www.zbmath.org/authors/?q=ai:gorbatenko.mikhail-v"Neznamov, V. P."https://www.zbmath.org/authors/?q=ai:neznamov.vasily-pSummary: We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider interactions of scalar particles, photons, and fermions with nonextremal rotating charged black holes in a minimal five-dimensional gauge supergravity. We analyze the behavior of effective potentials in second-order relativistic Schrödinger-type equations. In all cases, we establish the existence of the regime of particles ``falling'' on event horizons. An alternative can be collapsars with fermions in stationary bound states without a regime of particles ``falling''.Heat kernel: proper-time method, Fock-Schwinger gauge, path integral, and Wilson line.https://www.zbmath.org/1453.810482021-02-27T13:50:00+00:00"Ivanov, A. V."https://www.zbmath.org/authors/?q=ai:ivanov.aleksandr-valentinovich"Kharuk, N. V."https://www.zbmath.org/authors/?q=ai:kharuk.n-vSummary: This paper is devoted to the proper-time method and describes a model case that reflects the subtleties of constructing the heat kernel, is easily extended to more general cases (curved space, manifold with a boundary), and contains two interrelated parts: an asymptotic expansion and a path integral representation. We discuss the significance of gauge conditions and the role of ordered exponentials in detail, derive a new nonrecursive formula for the Seeley-DeWitt coefficients on the diagonal, and show the equivalence of two main approaches using the exponential formula.Coincidences between Calabi-Yau manifolds of Berglund-Hübsch type and Batyrev polytopes.https://www.zbmath.org/1453.810512021-02-27T13:50:00+00:00"Belavin, A. A."https://www.zbmath.org/authors/?q=ai:belavin.aleksandr-abramovich"Belakovskiy, M. Yu."https://www.zbmath.org/authors/?q=ai:belakovskiy.m-yuSummary: We consider the phenomenon of the complete coincidence of key properties of Calabi-Yau manifolds realized as hypersurfaces in two different weighted projective spaces. More precisely, the first manifold in such a pair is realized as a hypersurface in a weighted projective space, and the second is realized as a hypersurface in an orbifold of another weighted projective space. The two manifolds in each pair have the same Hodge numbers and the same geometry on the complex structure moduli space and are also associated with the same \(N=2\) gauged linear sigma model. We explain these coincidences using the correspondence between Calabi-Yau manifolds and the Batyrev reflexive polyhedra.