Koizumi, Hiroyasu; Ishikawa, Alto Theory of supercurrent in superconductors. (English) Zbl 07312226 Int. J. Mod. Phys. B 34, No. 31, Article ID 2030001, 42 p. (2020). MSC: 82D55 81Q70 PDF BibTeX XML Cite \textit{H. Koizumi} and \textit{A. Ishikawa}, Int. J. Mod. Phys. B 34, No. 31, Article ID 2030001, 42 p. (2020; Zbl 07312226) Full Text: DOI
Chen, Zeqian Observable-geometric phases and quantum computation. (English) Zbl 1435.81084 Int. J. Theor. Phys. 59, No. 4, 1255-1276 (2020). MSC: 81Q70 81P68 PDF BibTeX XML Cite \textit{Z. Chen}, Int. J. Theor. Phys. 59, No. 4, 1255--1276 (2020; Zbl 1435.81084) Full Text: DOI
Cornean, Horia D.; Gontier, David; Levitt, Antoine; Monaco, Domenico Localised Wannier functions in metallic systems. (English) Zbl 1412.35280 Ann. Henri Poincaré 20, No. 4, 1367-1391 (2019). MSC: 35Q40 81Q30 81Q70 82D35 PDF BibTeX XML Cite \textit{H. D. Cornean} et al., Ann. Henri Poincaré 20, No. 4, 1367--1391 (2019; Zbl 1412.35280) Full Text: DOI
Sun, Xin Application of connection in molecular dynamics. (English) Zbl 1391.81088 Commun. Theor. Phys. 69, No. 3, 308-310. (2018). MSC: 81Q70 81V55 PDF BibTeX XML Cite \textit{X. Sun}, Commun. Theor. Phys. 69, No. 3, 308--310. (2018; Zbl 1391.81088) Full Text: DOI
Wu, Siye Symmetry, phases and quantisation. (English) Zbl 1381.53163 Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 18th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 3–8, 2016. Sofia: Avangard Prima. Geometry, Integrability and Quantization, 77-96 (2017). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 53D50 32M15 53D12 81Q70 PDF BibTeX XML Cite \textit{S. Wu}, in: Proceedings of the 18th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 3--8, 2016. Sofia: Avangard Prima. 77--96 (2017; Zbl 1381.53163) Full Text: DOI
Monaco, Domenico; Tauber, Clément Gauge-theoretic invariants for topological insulators: a bridge between Berry, Wess-Zumino, and Fu-Kane-Mele. (English) Zbl 1370.35093 Lett. Math. Phys. 107, No. 7, 1315-1343 (2017). MSC: 35J10 81Q30 81Q70 PDF BibTeX XML Cite \textit{D. Monaco} and \textit{C. Tauber}, Lett. Math. Phys. 107, No. 7, 1315--1343 (2017; Zbl 1370.35093) Full Text: DOI
Nagy, Ákos The Berry connection of the Ginzburg-Landau vortices. (English) Zbl 1362.35291 Commun. Math. Phys. 350, No. 1, 105-128 (2017). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q56 35B40 82D55 PDF BibTeX XML Cite \textit{Á. Nagy}, Commun. Math. Phys. 350, No. 1, 105--128 (2017; Zbl 1362.35291) Full Text: DOI arXiv
Panzhenskii, V. I.; Surina, O. P. Finsler generalization of the Tamm metric. (English. Russian original) Zbl 1361.81109 Theor. Math. Phys. 189, No. 2, 1563-1573 (2016); translation from Teor. Mat. Fiz. 189, No. 2, 186-197 (2016). MSC: 81T20 81Q70 53B40 53C05 53C22 53B50 PDF BibTeX XML Cite \textit{V. I. Panzhenskii} and \textit{O. P. Surina}, Theor. Math. Phys. 189, No. 2, 1563--1573 (2016; Zbl 1361.81109); translation from Teor. Mat. Fiz. 189, No. 2, 186--197 (2016) Full Text: DOI
Zucchini, Roberto On higher holonomy invariants in higher gauge theory. II. (English) Zbl 1364.81197 Int. J. Geom. Methods Mod. Phys. 13, No. 7, Article ID 1650091, 22 p. (2016). Reviewer: Vida Milani (North Logan) MSC: 81T20 81Q70 81T13 57M25 57M27 14F35 14F40 PDF BibTeX XML Cite \textit{R. Zucchini}, Int. J. Geom. Methods Mod. Phys. 13, No. 7, Article ID 1650091, 22 p. (2016; Zbl 1364.81197) Full Text: DOI arXiv
Molitor, Mathieu Exponential families, Kähler geometry and quantum mechanics. (English) Zbl 1283.53072 J. Geom. Phys. 70, 54-80 (2013). MSC: 53C80 53C55 81Q70 62B10 PDF BibTeX XML Cite \textit{M. Molitor}, J. Geom. Phys. 70, 54--80 (2013; Zbl 1283.53072) Full Text: DOI arXiv
E, Weinan; Lu, Jian-feng; Yang, Xu Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase. (English) Zbl 1278.81084 Acta Math. Appl. Sin., Engl. Ser. 29, No. 3, 465-476 (2013). MSC: 81Q20 81Q05 35Q40 81Q70 81V70 PDF BibTeX XML Cite \textit{W. E} et al., Acta Math. Appl. Sin., Engl. Ser. 29, No. 3, 465--476 (2013; Zbl 1278.81084) Full Text: DOI
Esposito, Giampiero (ed.); Messina, Antonio (ed.); Vitale, Patricia (ed.) Special issue: Proceedings of the conference “Folding and unfolding: Interactions from geometry” in honor of Professor Giuseppe Marmo’s 65th birthday, Ischia, Italy, June 8–12, 2011. (English) Zbl 1250.81008 Int. J. Geom. Methods Mod. Phys. 9, No. 2, not consecutively paged (2012). MSC: 81-06 81Q70 35Q40 53C80 00B25 PDF BibTeX XML Cite \textit{G. Esposito} (ed.) et al., Int. J. Geom. Methods Mod. Phys. 9, No. 2, not consecutively paged (2012; Zbl 1250.81008)
Koizumi, Hiroyasu Persistent current generation by a Berry phase. (English) Zbl 1206.81051 J. Phys. A, Math. Theor. 43, No. 35, Article ID 354009, 13 p. (2010). Reviewer: I. A. Parinov (Rostov-na-Donu) MSC: 81Q70 82D55 81Q05 PDF BibTeX XML Cite \textit{H. Koizumi}, J. Phys. A, Math. Theor. 43, No. 35, Article ID 354009, 13 p. (2010; Zbl 1206.81051) Full Text: DOI
Eskin, G. Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach. (English) Zbl 1193.58014 Commun. Math. Phys. 284, No. 2, 317-343 (2008). Reviewer: Jean-Marc Bouclet (Toulouse) MSC: 58J45 81Q70 35Q40 35R30 PDF BibTeX XML Cite \textit{G. Eskin}, Commun. Math. Phys. 284, No. 2, 317--343 (2008; Zbl 1193.58014) Full Text: DOI arXiv
Melli, Juan B.; Rowley, Clarence W.; Rufat, Dzhelil S. Motion planning for an articulated body in a perfect planar fluid. (English) Zbl 1210.81041 SIAM J. Appl. Dyn. Syst. 5, No. 4, 650-669 (2006). MSC: 81Q70 53C29 55R10 PDF BibTeX XML Cite \textit{J. B. Melli} et al., SIAM J. Appl. Dyn. Syst. 5, No. 4, 650--669 (2006; Zbl 1210.81041) Full Text: DOI
Ito, Hiroshi T.; Tamura, Hideo Semiclassical analysis for magnetic scattering by two solenoidal fields. (English) Zbl 1109.81034 J. Lond. Math. Soc., II. Ser. 74, No. 3, 695-716 (2006). MSC: 81Q20 81Q70 81U99 35P25 35Q40 PDF BibTeX XML Cite \textit{H. T. Ito} and \textit{H. Tamura}, J. Lond. Math. Soc., II. Ser. 74, No. 3, 695--716 (2006; Zbl 1109.81034) Full Text: DOI
Aguilar, M. A.; Isidro, J. M.; Socolovsky, M. Moduli space of potentials in the Aharonov-Bohm effect. (English) Zbl 1169.81336 Adv. Appl. Clifford Algebr. 14, No. 1, 179-184 (2004). MSC: 81Q70 53C07 53C80 57N16 PDF BibTeX XML Cite \textit{M. A. Aguilar} et al., Adv. Appl. Clifford Algebr. 14, No. 1, 179--184 (2004; Zbl 1169.81336) Full Text: DOI
Lisok, A. L.; Trifonov, A. Yu.; Shapovalov, A. V. The evolution operator of the Hartree-type equation with a quadratic potential. (English) Zbl 1051.35060 J. Phys. A, Math. Gen. 37, No. 16, 4535-4556 (2004). MSC: 35Q40 81Q05 35Q55 81Q20 81Q70 PDF BibTeX XML Cite \textit{A. L. Lisok} et al., J. Phys. A, Math. Gen. 37, No. 16, 4535--4556 (2004; Zbl 1051.35060) Full Text: DOI arXiv
Chruściński, Dariusz; Jamiołkowski, Andrzej Geometric phases in classical and quantum mechanics. (English) Zbl 1075.81002 Progress in Mathematical Physics 36. Boston, MA: Birkhäuser (ISBN 0-8176-4282-X/hbk). xii, 333 p. (2004). Reviewer: Michael Keyl (Braunschweig) MSC: 81-02 81Q70 70G45 70-02 53C29 53C80 53D05 70H33 PDF BibTeX XML Cite \textit{D. Chruściński} and \textit{A. Jamiołkowski}, Geometric phases in classical and quantum mechanics. Boston, MA: Birkhäuser (2004; Zbl 1075.81002)
Kuwabara, Kuishi Spectral geometry for Schrödinger operators in a magnetic field focusing on geometrical and dynamical structures on manifolds. (English. Japanese original) Zbl 1122.58303 Nomizu, Katsumi (ed.), Selected papers on analysis and differential equations. Transl. from the Japanese by Katsumi Nomizu. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3508-4/hbk). Transl., Ser. 2, Am. Math. Soc. 211, 37-46 (2003); translation from Sūgaku 54, No. 1, 37-57 (2002). MSC: 58J50 35P20 35Q40 81Q70 PDF BibTeX XML
Pati, Arun K. Geometric phases for mixed states during unitary and non-unitary evolutions. (English) Zbl 1069.81513 Int. J. Quantum Inf. 1, No. 1, 135-152 (2003). MSC: 81P68 81Q70 47B65 PDF BibTeX XML Cite \textit{A. K. Pati}, Int. J. Quantum Inf. 1, No. 1, 135--152 (2003; Zbl 1069.81513) Full Text: DOI
Aguilar, M. A.; Socolovsky, M. Aharonov–Bohm effect, flat connections, and Green’s theorem. (English) Zbl 1001.81031 Int. J. Theor. Phys. 41, No. 5, 839-860 (2002). Reviewer: Paninjukunnath Achuthan (Chennai) MSC: 81Q70 53C29 83C60 PDF BibTeX XML Cite \textit{M. A. Aguilar} and \textit{M. Socolovsky}, Int. J. Theor. Phys. 41, No. 5, 839--860 (2002; Zbl 1001.81031) Full Text: DOI
Berry, M. V.; Dennis, M. R. Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in \(2+1\) spacetime. (English) Zbl 0997.35097 J. Phys. A, Math. Gen. 34, No. 42, 8877-8888 (2001). MSC: 35Q60 35J05 78A60 81Q70 PDF BibTeX XML Cite \textit{M. V. Berry} and \textit{M. R. Dennis}, J. Phys. A, Math. Gen. 34, No. 42, 8877--8888 (2001; Zbl 0997.35097) Full Text: DOI
Spohn, Herbert; Teufel, Stefan Adiabatic decoupling and time-dependent Born-Oppenheimer theory. (English) Zbl 1017.81014 Commun. Math. Phys. 224, No. 1, 113-132 (2001). Reviewer: Michael Perelmuter (Kyïv) MSC: 81Q20 81V55 81Q70 47N50 PDF BibTeX XML Cite \textit{H. Spohn} and \textit{S. Teufel}, Commun. Math. Phys. 224, No. 1, 113--132 (2001; Zbl 1017.81014) Full Text: DOI arXiv
Corach, Gustavo; Maestripieri, Alejandra L. Geometry of positive operators and Uhlmann’s approach to the geometric phase. (English) Zbl 0978.81037 Rep. Math. Phys. 47, No. 2, 287-299 (2001). MSC: 81Q70 81R15 58B99 PDF BibTeX XML Cite \textit{G. Corach} and \textit{A. L. Maestripieri}, Rep. Math. Phys. 47, No. 2, 287--299 (2001; Zbl 0978.81037) Full Text: DOI
Berry, M. V.; Dennis, M. R. Phase singularities in isotropic random waves. (English) Zbl 0978.35072 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 2001, 2059-2079 (2000). MSC: 35Q60 78A40 81Q70 PDF BibTeX XML Cite \textit{M. V. Berry} and \textit{M. R. Dennis}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 456, No. 2001, 2059--2079 (2000; Zbl 0978.35072) Full Text: DOI
Mangiarotti, L.; Sardanashvily, G. Connections in classical and quantum field theory. (English) Zbl 1053.53022 Singapore: World Scientific (ISBN 981-02-2013-8/hbk). x, 504 p. (2000). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 53-02 53C05 53D50 53D55 58-02 70Sxx 81T70 81T75 PDF BibTeX XML Cite \textit{L. Mangiarotti} and \textit{G. Sardanashvily}, Connections in classical and quantum field theory. Singapore: World Scientific (2000; Zbl 1053.53022)
Maamache, M. Unitary transformation approach to the exact solution for a class of time-dependent nonlinear Hamiltonian systems. (English) Zbl 0908.35110 J. Math. Phys. 39, No. 1, 161-169 (1998). MSC: 35Q40 81Q05 58J72 PDF BibTeX XML Cite \textit{M. Maamache}, J. Math. Phys. 39, No. 1, 161--169 (1998; Zbl 0908.35110) Full Text: DOI
Saradzhev, Fuad M. Berry phase in generalized chiral \(\text{QED}_2\). (English) Zbl 0939.81005 J. Phys. A, Math. Gen. 30, No. 6, 2219-2233 (1997). MSC: 81Q70 81V10 81T13 81T40 PDF BibTeX XML Cite \textit{F. M. Saradzhev}, J. Phys. A, Math. Gen. 30, No. 6, 2219--2233 (1997; Zbl 0939.81005) Full Text: DOI arXiv
Lai, Y.-Z.; Liang, J.-Q.; Müller-Kirsten, H. J. W.; Zhou, Jiange Time evolution of quantum systems with time-dependent Hamiltonian and the invariant Hermitian operator. (English) Zbl 0914.35109 J. Phys. A, Math. Gen. 29, No. 8, 1773-1783 (1996). MSC: 35Q40 81Q05 81V80 81R30 PDF BibTeX XML Cite \textit{Y. Z. Lai} et al., J. Phys. A, Math. Gen. 29, No. 8, 1773--1783 (1996; Zbl 0914.35109) Full Text: DOI
Maderner, W. Adiabatic connection and Schwinger term for two-dimensional Majorana-Weyl fermions in static background geometries. (English) Zbl 0845.53053 Rep. Math. Phys. 34, No. 2, 181-210 (1994). Reviewer: M.Kummer (Toledo) MSC: 53Z05 81T10 PDF BibTeX XML Cite \textit{W. Maderner}, Rep. Math. Phys. 34, No. 2, 181--210 (1994; Zbl 0845.53053) Full Text: DOI
Wu, Yihren On the quantization of the planar \(N\)-point vortex problem. (English) Zbl 0774.76020 J. Math. Phys. 34, No. 6, 2342-2352 (1993). MSC: 76B47 58D30 81S99 PDF BibTeX XML Cite \textit{Y. Wu}, J. Math. Phys. 34, No. 6, 2342--2352 (1993; Zbl 0774.76020) Full Text: DOI
Bohm, Arno; Boya, Luis J.; Kendrick, Brian On the uniqueness of the Berry connection. (English) Zbl 0768.57016 J. Math. Phys. 33, No. 7, 2528-2532 (1992). MSC: 57R99 81Q99 53C05 55R10 PDF BibTeX XML Cite \textit{A. Bohm} et al., J. Math. Phys. 33, No. 7, 2528--2532 (1992; Zbl 0768.57016) Full Text: DOI
Papadopoulos, George A generalization of Berry’s connection. (English) Zbl 0769.58059 J. Phys. A, Math. Gen. 25, No. 7, 2071-2076 (1992). Reviewer: R.Schmid (Atlanta) MSC: 58Z05 81Q10 PDF BibTeX XML Cite \textit{G. Papadopoulos}, J. Phys. A, Math. Gen. 25, No. 7, 2071--2076 (1992; Zbl 0769.58059) Full Text: DOI
Hagedorn, George A. Time-reversal invariance and the time-dependent Born-Oppenheimer approximation. (English) Zbl 0796.47053 Fulling, S. A. (ed.) et al., Forty more years of ramifications: spectral asymptotics and its applications. College Station, TX: Texas A&M University, Dept. of Mathematics. Discourses Math. Appl. 1, 161-197 (1991). MSC: 47N50 81Q20 PDF BibTeX XML Cite \textit{G. A. Hagedorn}, Discourses Math. Appl. 1, 161--197 (1991; Zbl 0796.47053)
Kvitsinsky, Andrei; Putterman, Seth Adiabatic evolution of an irreversible two level system. (English) Zbl 0736.35089 J. Math. Phys. 32, No. 5, 1403-1407 (1991). MSC: 35Q40 PDF BibTeX XML Cite \textit{A. Kvitsinsky} and \textit{S. Putterman}, J. Math. Phys. 32, No. 5, 1403--1407 (1991; Zbl 0736.35089) Full Text: DOI
Giavarini, G.; Onofri, E. Vector coherent states and non-Abelian gauge structures in quantum mechanics. (English) Zbl 0733.22014 Int. J. Mod. Phys. A 5, No. 22, 4311-4331 (1990). Reviewer: J.Asch (Berlin) MSC: 22E70 81R30 35Q40 PDF BibTeX XML Cite \textit{G. Giavarini} and \textit{E. Onofri}, Int. J. Mod. Phys. A 5, No. 22, 4311--4331 (1990; Zbl 0733.22014) Full Text: DOI
Brihaye, Y.; Giler, S.; Kosiński, P.; Maślanka, P. A note on non-integrable phases and coherent states. (English) Zbl 0715.35069 J. Phys. A, Math. Gen. 23, No. 11, 1985-1991 (1990). Reviewer: Y.Brihaye MSC: 35Q40 22E70 81Q05 PDF BibTeX XML Cite \textit{Y. Brihaye} et al., J. Phys. A, Math. Gen. 23, No. 11, 1985--1991 (1990; Zbl 0715.35069) Full Text: DOI
Marsden, J. E.; Montgomery, R.; Ratiu, T. Reduction, symmetry, and phases in mechanics. (English) Zbl 0713.58052 Mem. Am. Math. Soc. 436, 110 p. (1990). Reviewer: P.Khmelevskaja MSC: 37-XX 70H33 PDF BibTeX XML Cite \textit{J. E. Marsden} et al., Reduction, symmetry, and phases in mechanics. Providence, RI: American Mathematical Society (AMS) (1990; Zbl 0713.58052) Full Text: DOI
Weinstein, Alan Connections of Berry and Hannay type for moving Lagrangian submanifolds. (English) Zbl 0713.58015 Adv. Math. 82, No. 2, 133-159 (1990). Reviewer: J.Koiller MSC: 37J99 53C07 53C15 PDF BibTeX XML Cite \textit{A. Weinstein}, Adv. Math. 82, No. 2, 133--159 (1990; Zbl 0713.58015) Full Text: DOI
Bednarz, Bernard F. Geometric methods and the gauge structure of Berry’s phase. (English) Zbl 0723.35067 Int. J. Mod. Phys. A 4, No. 16, 4203-4211 (1989). Reviewer: J.Asch (Berlin) MSC: 35Q40 81Q99 PDF BibTeX XML Cite \textit{B. F. Bednarz}, Int. J. Mod. Phys. A 4, No. 16, 4203--4211 (1989; Zbl 0723.35067) Full Text: DOI
Mondragon, R. J.; Berry, M. V. The quantum phase 2-form near degeneracies: Two numerical studies. (English) Zbl 0706.35117 Proc. R. Soc. Lond., Ser. A 424, No. 1867, 263-278 (1989). Reviewer: J.Asch MSC: 35Q40 65N25 35P05 PDF BibTeX XML Cite \textit{R. J. Mondragon} and \textit{M. V. Berry}, Proc. R. Soc. Lond., Ser. A 424, No. 1867, 263--278 (1989; Zbl 0706.35117) Full Text: DOI
Golin, Simon; Knauf, Andreas; Marmi, Stefano Hannay angles: Existence and geometrical interpretation. (English) Zbl 0744.70021 Nonlinear dynamics, Proc. Conf., Bologna/Italy 1988, 200-209 (1989). MSC: 70H05 70F15 37J99 81Q99 PDF BibTeX XML Cite \textit{S. Golin} et al., in: Conference on nonlinear dynamics, Bologna, Italy, 30 May-3 June 1988. Singapore etc.: World Scientific. 200--209 (1989; Zbl 0744.70021)
Avron, J. E.; Sadun, L.; Segert, J.; Simon, B. Chern numbers, quaternions, and Berry’s phases in Fermi systems. (English) Zbl 0830.57020 Commun. Math. Phys. 124, No. 4, 595-627 (1989). Reviewer: H.Hogreve (MR 91e:81029) MSC: 57R99 58J90 57R57 57R20 PDF BibTeX XML Cite \textit{J. E. Avron} et al., Commun. Math. Phys. 124, No. 4, 595--627 (1989; Zbl 0830.57020) Full Text: DOI