## Arnold, Anton

Compute Distance To:
 Author ID: arnold.anton Published as: Arnold, Anton; Arnold, A.
 Documents Indexed: 83 Publications since 1989 8 Contributions as Editor Co-Authors: 77 Co-Authors with 83 Joint Publications 2,123 Co-Co-Authors
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### Co-Authors

 7 single-authored 11 Markowich, Peter Alexander 10 Ehrhardt, Matthias 7 Carlen, Eric Anders 6 Carrillo de la Plata, José Antonio 6 Desvillettes, Laurent 6 Stürzer, Dominik 5 Toscani, Giuseppe 4 Achleitner, Franz 4 Martínez Gamba, Irene 4 Ringhofer, Christian A. 3 Ben Abdallah, Naoufel 3 Degond, Pierre 3 Dhamo, Elidon 3 Dolbeault, Jean 3 Hammer, René 3 Manzini, Chiara 3 Miletić, Maja 3 Pötz, Walter 3 Schulte, Maike 3 Signorello, Beatrice 3 Unterreiter, Andreas 3 Wöhrer, Tobias 2 Döpfner, Kirian 2 Einav, Amit 2 Glassey, Robert T. 2 Jüngel, Ansgar 2 Kim, Jinmyong 2 Koprucki, Thomas 2 Kugi, Andreas 2 Levermore, C. David 2 Mauser, Norbert Julius 2 Negulescu, Claudia 2 Nier, Francis 2 Sparber, Christof 2 Steinrück, Herbert 2 Yao, Xiaohua 2 Zisowsky, Andrea 1 Amodio, Pierluigi 1 Antoine, Xavier 1 Bartier, Jean-Philippe 1 Besse, Christophe 1 Bian, Lei 1 Bonilla, Luis Lopez 1 Cercignani, Carlo 1 Drmota, Michael 1 Fagnola, Franco 1 Geevers, Sjoerd 1 Geier, J. 1 Giering, Ulrich 1 Gualdani, Maria Pia 1 Ju, Qiangchang 1 Kanta, M. 1 Klapproth, Corinna 1 Klein, Christian 1 Körner, Jannis 1 Krob, Daniel 1 Lange, Horst 1 Lederman, Claudia B. 1 Levitina, Tatiana V. 1 López, José Luis 1 Mischler, Stéphane 1 Mouhot, Clément 1 Pang, Gang 1 Perugia, Ilaria 1 Pietra, Paola 1 Prévost, Céline 1 Schädle, Achim 1 Schmeiser, Christian 1 Schmock, Uwe 1 Settanni, Giuseppina 1 Shu, Chi-Wang 1 Soler, Juan S. 1 Tang, Shaoqiang 1 Tidriri, Moulay D. 1 Ujvari, Bernhard 1 Viertl, Reinhard Karl Wolfgang 1 Villani, Cédric 1 Weinmüller, Ewa B. 1 Zweifel, Paul F.
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### Serials

 5 Journal of Computational Physics 5 Communications in Mathematical Sciences 4 Transport Theory and Statistical Physics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Oberwolfach Reports 3 Computers & Mathematics with Applications 3 Journal of Mathematical Analysis and Applications 3 Monatshefte für Mathematik 3 SIAM Journal on Numerical Analysis 3 Kinetic and Related Models 2 Journal of Differential Equations 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Communications in Partial Differential Equations 2 The IMA Volumes in Mathematics and its Applications 1 Communications in Mathematical Physics 1 International Journal of Control 1 Information Processing Letters 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 BIT 1 Calcolo 1 IEEE Transactions on Automatic Control 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Revista Matemática Iberoamericana 1 Internationale Mathematische Nachrichten 1 Applied Mathematics Letters 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Rivista di Matematica della Università di Parma. Serie 6 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Communications in Computational Physics 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Communications on Stochastic Analysis 1 Rivista di Matematica della Università di Parma. New Series 1 Nanosistemy: Fizika, Khimiya, Matematika
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### Fields

 61 Partial differential equations (35-XX) 31 Statistical mechanics, structure of matter (82-XX) 30 Numerical analysis (65-XX) 26 Quantum theory (81-XX) 10 Ordinary differential equations (34-XX) 9 Operator theory (47-XX) 7 General and overarching topics; collections (00-XX) 7 Fluid mechanics (76-XX) 6 Integral equations (45-XX) 4 Mechanics of deformable solids (74-XX) 3 Real functions (26-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Probability theory and stochastic processes (60-XX) 2 Optics, electromagnetic theory (78-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

67 Publications have been cited 956 times in 646 Documents Cited by Year
On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Zbl 0982.35113
Arnold, Anton; Markowich, Peter; Toscani, Giuseppe; Unterreiter, Andreas
2001
A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178
Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim
2008
Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability. Zbl 1085.65513
Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan
2003
Discrete transparent boundary conditions for the Schrödinger equation. Zbl 0993.65097
Ehrhardt, M.; Arnold, A.
2001
On generalized Csiszár-Kullback inequalities. Zbl 1015.94003
Unterreiter, Andreas; Arnold, Anton; Markowich, Peter; Toscani, Giuseppe
2000
Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109
Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C.
2004
Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics. Zbl 0915.76081
Arnold, Anton; Ehrhardt, Matthias
1998
Self-consistent relaxation-time models in quantum mechanics. Zbl 0849.35113
Arnold, Anton
1996
An analysis of quantum Fokker-Planck models: a Wigner function approach. Zbl 1062.35097
Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan
2004
Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Zbl 1303.92091
Arnold, Anton; Desvillettes, Laurent; Prévost, Céline
2012
Mathematical concepts of open quantum boundary conditions. Zbl 1019.81010
Arnold, Anton
2001
On large time asymptotics for drift-diffusion-Poisson systems. Zbl 1017.82041
Arnold, Anton; Markowich, Peter; Toscani, Giuseppe
2000
Large-time behavior in non-symmetric Fokker-Planck equations. Zbl 1342.35394
Achleitner, Franz; Arnold, Anton; Stürzer, Dominik
2015
A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in $$(1+1)$$D. Zbl 1349.81085
Hammer, René; Pötz, Walter; Arnold, Anton
2014
Interpolation between logarithmic Sobolev and Poincaré inequalities. Zbl 1146.60063
Arnold, Anton; Bartier, Jean-Philippe; Dolbeault, Jean
2007
An operator splitting method for the Wigner-Poisson problem. Zbl 0860.65143
Arnold, Anton; Ringhofer, Christian
1996
Refined convex Sobolev inequalities. Zbl 1087.35018
Arnold, Anton; Dolbeault, Jean
2005
Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems. Zbl 1106.82381
Arnold, A.; Carrillo, J. A.; Gamba, I.; Shu, C.-W.
2001
Large-time behavior of non-symmetric Fokker-Planck type equations. Zbl 1331.82042
Arnold, Anton; Carlen, Eric; Ju, Qiangchang
2008
The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Zbl 0742.35078
Arnold, Anton; Nier, Francis
1991
Global estimates of fundamental solutions for higher-order Schrödinger equations. Zbl 1256.35106
Kim, JinMyong; Arnold, Anton; Yao, Xiaohua
2012
Refined long-time asymptotics for some polymeric fluid flow models. Zbl 1213.35094
Arnold, A.; Carrillo, J. A.; Manzini, C.
2010
Discrete transparent boundary conditions for the Schrödinger equation – a compact higher order scheme. Zbl 1145.65058
Schulte, Maike; Arnold, Anton
2008
Mathematical properties of quantum evolution equations. Zbl 1170.82372
Arnold, Anton
2008
The “electromagnetic” Wigner equation for an electron with spin. Zbl 0701.35130
Arnold, Anton; Steinrück, Herbert
1989
WKB-based schemes for the oscillatory 1D Schrödinger equation in the semiclassical limit. Zbl 1230.65078
Arnold, Anton; Ben Abdallah, Naoufel; Negulescu, Claudia
2011
The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects. Zbl 1121.82031
Arnold, Anton; Dhamo, Elidon; Manzini, Chiara
2007
A discrete-velocity, stationary Wigner equation. Zbl 1019.82020
Arnold, Anton; Lange, Horst; Zweifel, Paul F.
2000
Quantum dynamical semigroups for diffusion models with Hartree interaction. Zbl 1085.82004
Arnold, A.; Sparber, C.
2004
On linear hypocoercive BGK models. Zbl 1353.35113
Achleitner, Franz; Arnold, Anton; Carlen, Eric A.
2016
Single-cone real-space finite difference scheme for the time-dependent Dirac equation. Zbl 1349.65301
Hammer, René; Pötz, Walter; Arnold, Anton
2014
Discrete transparent boundary conditions for the Schrödinger equation on circular domains. Zbl 1256.35103
Arnold, Anton; Ehrhardt, Matthias; Schulte, Maike; Sofronov, Ivan
2012
On absorbing boundary conditions for quantum transport equations. Zbl 0821.45002
Arnold, Anton
1994
On multi-dimensional hypocoercive BGK models. Zbl 1405.82023
Achleitner, Franz; Arnold, Anton; Carlen, Eric A.
2018
The Wigner-Fokker-Planck equation: stationary states and large time behavior. Zbl 1253.82065
Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof
2012
Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system. Zbl 1359.93399
Miletić, Maja; Stürzer, Dominik; Arnold, Anton; Kugi, Andreas
2016
Dispersive effects in quantum kinetic equations. Zbl 1161.35040
Arnold, Anton; Dhamo, Elidon; Manzini, Chiara
2007
Operator splitting methods applied to spectral discretizations of quantum transport equations. Zbl 0847.65074
Arnold, Anton; Ringhofer, Christian
1995
Quantum Fokker-Planck models: the Lindblad and Wigner approaches. Zbl 1180.81089
Arnold, A.; Fagnola, F.; Neumann, L.
2008
Discrete transparent boundary conditions for transient $$kp$$-Schrödinger equations with application to quantum heterostructures. Zbl 1080.65080
Zisowsky, Andrea; Arnold, Anton; Ehrhardt, Matthias; Koprucki, Thomas
2005
On the periodic Wigner–Poisson–Fokker–Planck system. Zbl 1014.35084
Arnold, Anton; Carrillo, Jose A.; Dhamo, Elidon
2002
On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations. Zbl 1387.35579
Arnold, Anton; Einav, Amit; Wöhrer, Tobias
2018
The one-dimensional periodic Bloch-Poisson equation. Zbl 0828.34073
Arnold, Anton; Markowich, Peter A.; Mauser, Norbert
1991
Entropy decay of discretized Fokker-Planck equations. I: Temporal semidiscretization. Zbl 1053.82025
Arnold, A.; Unterreiter, A.
2003
Transparent boundary conditions for quantum-waveguide simulations. Zbl 1159.82326
Arnold, Anton; Schulte, Maike
2008
Estimates for a class of oscillatory integrals and decay rates for wave-type equations. Zbl 1248.35032
Arnold, Anton; Kim, JinMyong; Yao, Xiaohua
2012
On optimal decay estimates for ODEs and PDEs with modal decomposition. Zbl 1442.82028
Achleitner, Franz; Arnold, Anton; Signorello, Beatrice
2019
Improved entropy decay estimates for the heat equation. Zbl 1139.35012
Arnold, A.; Carrillo, J. A.; Klapproth, C.
2008
A piezoelectric Euler-Bernoulli beam with dynamic boundary control: stability and dissipative FEM. Zbl 1326.35034
Miletić, Maja; Arnold, Anton
2015
Multi-scale modeling of quantum semiconductor devices. Zbl 1366.82062
Arnold, Anton; Jüngel, Ansgar
2006
The Wigner-Poisson problem in a crystal. Zbl 0822.58070
Arnold, A.; Degond, P.; Markowich, P. A.; Steinrück, Herbert
1989
A generalized Bakry-Emery condition for non-symmetric diffusions. Zbl 0967.35057
Arnold, Anton; Carlen, Eric
2000
The relaxation-time Wigner equation. Zbl 0870.35085
Arnold, Anton
1995
An analysis of the Marshak conditions for matching Boltzmann and Euler equations. Zbl 0882.76078
Arnold, Anton; Giering, Ulrich
1997
Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. Zbl 1421.65020
Arnold, Anton; Negulescu, Claudia
2018
Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point. Zbl 1439.34078
Arnold, Anton; Döpfner, Kirian
2020
Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations. Zbl 1428.35036
Arnold, Anton; Jin, Shi; Wöhrer, Tobias
2020
Large-time behavior of discrete kinetic equations with non-symmetric interactions. Zbl 1033.35072
Arnold, Anton; Carrillo, Jose A.; Tidriri, Moulay D.
2002
Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation. Zbl 1066.65081
Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan
2005
An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Zbl 1329.35065
Miletić, Maja; Stürzer, Dominik; Arnold, Anton
2015
Numerical analysis of the deterministic particle method applied to the Wigner equation. Zbl 0763.65092
Arnold, Anton; Nier, Francis
1992
Spectral analysis and long-time behaviour of a Fokker-Planck equation with a non-local perturbation. Zbl 1291.35406
Stürzer, Dominik; Arnold, Anton
2014
The periodic quantum Liouville-Poisson problem. Zbl 0727.35113
Arnold, Anton; Markowich, Peter A.
1990
Almost exact boundary conditions for transient Schrödinger-Poisson system. Zbl 1349.65267
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016
Closed-loop stability analysis of a gantry crane with heavy chain and payload. Zbl 1397.93181
Stürzer, Dominik; Arnold, Anton; Kugi, Andreas
2018
Recognizable subsets of the two letter plactic monoid. Zbl 1337.68172
Arnold, A.; Kanta, M.; Krob, D.
1997
Large time convergence of the non-homogeneous Goldstein-Taylor equation. Zbl 1459.82259
Arnold, Anton; Einav, Amit; Signorello, Beatrice; Wöhrer, Tobias
2021
Large time convergence of the non-homogeneous Goldstein-Taylor equation. Zbl 1459.82259
Arnold, Anton; Einav, Amit; Signorello, Beatrice; Wöhrer, Tobias
2021
Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point. Zbl 1439.34078
Arnold, Anton; Döpfner, Kirian
2020
Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations. Zbl 1428.35036
Arnold, Anton; Jin, Shi; Wöhrer, Tobias
2020
On optimal decay estimates for ODEs and PDEs with modal decomposition. Zbl 1442.82028
Achleitner, Franz; Arnold, Anton; Signorello, Beatrice
2019
On multi-dimensional hypocoercive BGK models. Zbl 1405.82023
Achleitner, Franz; Arnold, Anton; Carlen, Eric A.
2018
On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations. Zbl 1387.35579
Arnold, Anton; Einav, Amit; Wöhrer, Tobias
2018
Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. Zbl 1421.65020
Arnold, Anton; Negulescu, Claudia
2018
Closed-loop stability analysis of a gantry crane with heavy chain and payload. Zbl 1397.93181
Stürzer, Dominik; Arnold, Anton; Kugi, Andreas
2018
On linear hypocoercive BGK models. Zbl 1353.35113
Achleitner, Franz; Arnold, Anton; Carlen, Eric A.
2016
Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system. Zbl 1359.93399
Miletić, Maja; Stürzer, Dominik; Arnold, Anton; Kugi, Andreas
2016
Almost exact boundary conditions for transient Schrödinger-Poisson system. Zbl 1349.65267
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016
Large-time behavior in non-symmetric Fokker-Planck equations. Zbl 1342.35394
Achleitner, Franz; Arnold, Anton; Stürzer, Dominik
2015
A piezoelectric Euler-Bernoulli beam with dynamic boundary control: stability and dissipative FEM. Zbl 1326.35034
Miletić, Maja; Arnold, Anton
2015
An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Zbl 1329.35065
Miletić, Maja; Stürzer, Dominik; Arnold, Anton
2015
A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in $$(1+1)$$D. Zbl 1349.81085
Hammer, René; Pötz, Walter; Arnold, Anton
2014
Single-cone real-space finite difference scheme for the time-dependent Dirac equation. Zbl 1349.65301
Hammer, René; Pötz, Walter; Arnold, Anton
2014
Spectral analysis and long-time behaviour of a Fokker-Planck equation with a non-local perturbation. Zbl 1291.35406
Stürzer, Dominik; Arnold, Anton
2014
Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Zbl 1303.92091
Arnold, Anton; Desvillettes, Laurent; Prévost, Céline
2012
Global estimates of fundamental solutions for higher-order Schrödinger equations. Zbl 1256.35106
Kim, JinMyong; Arnold, Anton; Yao, Xiaohua
2012
Discrete transparent boundary conditions for the Schrödinger equation on circular domains. Zbl 1256.35103
Arnold, Anton; Ehrhardt, Matthias; Schulte, Maike; Sofronov, Ivan
2012
The Wigner-Fokker-Planck equation: stationary states and large time behavior. Zbl 1253.82065
Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof
2012
Estimates for a class of oscillatory integrals and decay rates for wave-type equations. Zbl 1248.35032
Arnold, Anton; Kim, JinMyong; Yao, Xiaohua
2012
WKB-based schemes for the oscillatory 1D Schrödinger equation in the semiclassical limit. Zbl 1230.65078
Arnold, Anton; Ben Abdallah, Naoufel; Negulescu, Claudia
2011
Refined long-time asymptotics for some polymeric fluid flow models. Zbl 1213.35094
Arnold, A.; Carrillo, J. A.; Manzini, C.
2010
A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178
Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim
2008
Large-time behavior of non-symmetric Fokker-Planck type equations. Zbl 1331.82042
Arnold, Anton; Carlen, Eric; Ju, Qiangchang
2008
Discrete transparent boundary conditions for the Schrödinger equation – a compact higher order scheme. Zbl 1145.65058
Schulte, Maike; Arnold, Anton
2008
Mathematical properties of quantum evolution equations. Zbl 1170.82372
Arnold, Anton
2008
Quantum Fokker-Planck models: the Lindblad and Wigner approaches. Zbl 1180.81089
Arnold, A.; Fagnola, F.; Neumann, L.
2008
Transparent boundary conditions for quantum-waveguide simulations. Zbl 1159.82326
Arnold, Anton; Schulte, Maike
2008
Improved entropy decay estimates for the heat equation. Zbl 1139.35012
Arnold, A.; Carrillo, J. A.; Klapproth, C.
2008
Interpolation between logarithmic Sobolev and Poincaré inequalities. Zbl 1146.60063
Arnold, Anton; Bartier, Jean-Philippe; Dolbeault, Jean
2007
The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects. Zbl 1121.82031
Arnold, Anton; Dhamo, Elidon; Manzini, Chiara
2007
Dispersive effects in quantum kinetic equations. Zbl 1161.35040
Arnold, Anton; Dhamo, Elidon; Manzini, Chiara
2007
Multi-scale modeling of quantum semiconductor devices. Zbl 1366.82062
Arnold, Anton; Jüngel, Ansgar
2006
Refined convex Sobolev inequalities. Zbl 1087.35018
Arnold, Anton; Dolbeault, Jean
2005
Discrete transparent boundary conditions for transient $$kp$$-Schrödinger equations with application to quantum heterostructures. Zbl 1080.65080
Zisowsky, Andrea; Arnold, Anton; Ehrhardt, Matthias; Koprucki, Thomas
2005
Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation. Zbl 1066.65081
Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan
2005
Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109
Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C.
2004
An analysis of quantum Fokker-Planck models: a Wigner function approach. Zbl 1062.35097
Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan
2004
Quantum dynamical semigroups for diffusion models with Hartree interaction. Zbl 1085.82004
Arnold, A.; Sparber, C.
2004
Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability. Zbl 1085.65513
Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan
2003
Entropy decay of discretized Fokker-Planck equations. I: Temporal semidiscretization. Zbl 1053.82025
Arnold, A.; Unterreiter, A.
2003
On the periodic Wigner–Poisson–Fokker–Planck system. Zbl 1014.35084
Arnold, Anton; Carrillo, Jose A.; Dhamo, Elidon
2002
Large-time behavior of discrete kinetic equations with non-symmetric interactions. Zbl 1033.35072
Arnold, Anton; Carrillo, Jose A.; Tidriri, Moulay D.
2002
On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Zbl 0982.35113
Arnold, Anton; Markowich, Peter; Toscani, Giuseppe; Unterreiter, Andreas
2001
Discrete transparent boundary conditions for the Schrödinger equation. Zbl 0993.65097
Ehrhardt, M.; Arnold, A.
2001
Mathematical concepts of open quantum boundary conditions. Zbl 1019.81010
Arnold, Anton
2001
Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems. Zbl 1106.82381
Arnold, A.; Carrillo, J. A.; Gamba, I.; Shu, C.-W.
2001
On generalized Csiszár-Kullback inequalities. Zbl 1015.94003
Unterreiter, Andreas; Arnold, Anton; Markowich, Peter; Toscani, Giuseppe
2000
On large time asymptotics for drift-diffusion-Poisson systems. Zbl 1017.82041
Arnold, Anton; Markowich, Peter; Toscani, Giuseppe
2000
A discrete-velocity, stationary Wigner equation. Zbl 1019.82020
Arnold, Anton; Lange, Horst; Zweifel, Paul F.
2000
A generalized Bakry-Emery condition for non-symmetric diffusions. Zbl 0967.35057
Arnold, Anton; Carlen, Eric
2000
Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics. Zbl 0915.76081
Arnold, Anton; Ehrhardt, Matthias
1998
An analysis of the Marshak conditions for matching Boltzmann and Euler equations. Zbl 0882.76078
Arnold, Anton; Giering, Ulrich
1997
Recognizable subsets of the two letter plactic monoid. Zbl 1337.68172
Arnold, A.; Kanta, M.; Krob, D.
1997
Self-consistent relaxation-time models in quantum mechanics. Zbl 0849.35113
Arnold, Anton
1996
An operator splitting method for the Wigner-Poisson problem. Zbl 0860.65143
Arnold, Anton; Ringhofer, Christian
1996
Operator splitting methods applied to spectral discretizations of quantum transport equations. Zbl 0847.65074
Arnold, Anton; Ringhofer, Christian
1995
The relaxation-time Wigner equation. Zbl 0870.35085
Arnold, Anton
1995
On absorbing boundary conditions for quantum transport equations. Zbl 0821.45002
Arnold, Anton
1994
Numerical analysis of the deterministic particle method applied to the Wigner equation. Zbl 0763.65092
Arnold, Anton; Nier, Francis
1992
The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Zbl 0742.35078
Arnold, Anton; Nier, Francis
1991
The one-dimensional periodic Bloch-Poisson equation. Zbl 0828.34073
Arnold, Anton; Markowich, Peter A.; Mauser, Norbert
1991
The periodic quantum Liouville-Poisson problem. Zbl 0727.35113
Arnold, Anton; Markowich, Peter A.
1990
The “electromagnetic” Wigner equation for an electron with spin. Zbl 0701.35130
Arnold, Anton; Steinrück, Herbert
1989
The Wigner-Poisson problem in a crystal. Zbl 0822.58070
Arnold, A.; Degond, P.; Markowich, P. A.; Steinrück, Herbert
1989
all top 5

### Cited by 833 Authors

 31 Arnold, Anton 28 Dolbeault, Jean 22 Antoine, Xavier 17 Jüngel, Ansgar 15 Carrillo de la Plata, José Antonio 15 Zheng, Chunxiong 14 Toscani, Giuseppe 14 Zhang, Jiwei 13 Markowich, Peter Alexander 12 López, José Luis 11 Ehrhardt, Matthias 11 Lorin, Emmanuel 11 Méhats, Florian 10 Besse, Christophe 9 Tang, Shaoqiang 8 Degond, Pierre 8 Zlotnik, Alexander A. 7 Barletti, Luigi 7 Fellner, Klemens 7 Goudon, Thierry 7 Pang, Gang 7 Perthame, Benoît 7 Pinaud, Olivier 7 Wu, Xiaonan 6 Bao, Weizhu 6 Esteban, Maria J. 6 Frosali, Giovanni 6 Han, Houde 6 Lelièvre, Tony 6 Mirrahimi, Sepideh 5 Cai, Yongyong 5 Calvez, Vincent 5 Cañizo, José Alfredo 5 Chainais-Hillairet, Claire 5 Čiegis, Raimondas 5 Henderson, Christopher 5 Li, Jiyong 5 Manzini, Chiara 5 Montejo-Gámez, Jesús 5 Nieto, Juanjo 5 Petrov, Pavel S. 5 Soler, Juan S. 5 Tang, Qinglin 5 Yin, Jia 5 Zisowsky, Andrea 4 Barrett, John W. 4 Ben Abdallah, Naoufel 4 Bouin, Emeric 4 Carlen, Eric Anders 4 Desvillettes, Laurent 4 Di Francesco, Marco 4 Du, Qiang 4 Gentil, Ivan 4 Girardin, Léo 4 Huang, Zhongyi 4 Kowalczyk, Michał 4 Li, Bin 4 Liu, Hailiang 4 Lorenzi, Tommaso 4 Loss, Michael 4 Lu, Tiao 4 Mielke, Alexander 4 Noble, Pascal 4 Pavliotis, Grigorios A. 4 Pötz, Walter 4 Ringhofer, Christian A. 4 Saanouni, Tarek 4 Sparber, Christof 4 Stoltz, Gabriel 4 Süli, Endre E. 4 Tang, Bao Quoc 4 Vaibhav, Vishal 4 Vazquez, Juan Luis 4 Wang, Shu 4 Yang, Xu 3 Abounouh, Mostafa 3 Achleitner, Franz 3 Al Moatassime, Hassan 3 Bartier, Jean-Philippe 3 Bolley, François 3 Burger, Martin 3 Cancès, Clément 3 Carles, Rémi 3 Coulombel, Jean-François 3 Dang Quang A 3 Del Pino, Manuel A. 3 Dreher, Michael 3 Faraj, Ali 3 Friese, Tilmann 3 Furioli, Giulia 3 Gerasimenko, Viktor Ivanovich 3 Geuzaine, Christophe A. 3 Gualdani, Maria Pia 3 Guillin, Arnaud 3 Haskovec, Jan 3 Herda, Maxime 3 Ji, Songsong 3 Jia, Xiaowei 3 Jiang, Haiyan 3 Jiang, Shidong ...and 733 more Authors
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### Cited in 181 Serials

 55 Journal of Computational Physics 28 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 19 Journal of Statistical Physics 19 Journal of Scientific Computing 18 Journal of Differential Equations 18 Journal of Functional Analysis 15 Journal of Computational and Applied Mathematics 15 Kinetic and Related Models 14 Numerische Mathematik 14 Applied Numerical Mathematics 13 Journal of Mathematical Analysis and Applications 12 Journal of Mathematical Physics 11 Transport Theory and Statistical Physics 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Archive for Rational Mechanics and Analysis 10 Communications in Partial Differential Equations 10 SIAM Journal on Mathematical Analysis 9 Applied Mathematics Letters 8 SIAM Journal on Numerical Analysis 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Computers & Mathematics with Applications 7 Communications in Mathematical Physics 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Discrete and Continuous Dynamical Systems 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 SIAM Journal on Scientific Computing 5 Nonlinearity 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Mathematics and Computers in Simulation 5 Numerical Methods for Partial Differential Equations 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Doklady Mathematics 5 Multiscale Modeling & Simulation 5 Communications in Computational Physics 4 Applicable Analysis 4 International Journal of Control 4 Mathematical Methods in the Applied Sciences 4 Wave Motion 4 Mathematics of Computation 4 Chinese Annals of Mathematics. Series B 4 Mathematical and Computer Modelling 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Discrete and Continuous Dynamical Systems. Series B 3 Communications on Pure and Applied Mathematics 3 Bulletin of Mathematical Biology 3 The Annals of Probability 3 Applied Mathematics and Computation 3 Automatica 3 Monatshefte für Mathematik 3 Acta Applicandae Mathematicae 3 Physica D 3 Revista Matemática Iberoamericana 3 The Annals of Applied Probability 3 Numerical Algorithms 3 Journal of Nonlinear Science 3 Calculus of Variations and Partial Differential Equations 3 Annales Henri Poincaré 3 Frontiers of Mathematics in China 3 Science China. Mathematics 3 East Asian Journal on Applied Mathematics 3 Annales Henri Lebesgue 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Biology 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Quarterly of Applied Mathematics 2 Transactions of the American Mathematical Society 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Computational Mechanics 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 International Journal of Computer Mathematics 2 SIAM Journal on Applied Mathematics 2 Potential Analysis 2 Journal of Mathematical Sciences (New York) 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Interfaces and Free Boundaries 2 Nonlinear Analysis. Real World Applications 2 Mathematical Modelling and Analysis 2 Advanced Nonlinear Studies 2 International Journal of Computational Methods 2 Journal of Computational Acoustics 2 Boundary Value Problems 2 Research in the Mathematical Sciences 1 Modern Physics Letters B 1 Astrophysics and Space Science 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 General Relativity and Gravitation 1 Inverse Problems 1 Physica A 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Theory of Probability and its Applications 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 BIT ...and 81 more Serials
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### Cited in 43 Fields

 462 Partial differential equations (35-XX) 225 Numerical analysis (65-XX) 174 Statistical mechanics, structure of matter (82-XX) 102 Quantum theory (81-XX) 87 Fluid mechanics (76-XX) 58 Biology and other natural sciences (92-XX) 51 Probability theory and stochastic processes (60-XX) 40 Operator theory (47-XX) 30 Functional analysis (46-XX) 29 Integral equations (45-XX) 24 Real functions (26-XX) 24 Optics, electromagnetic theory (78-XX) 22 Dynamical systems and ergodic theory (37-XX) 19 Ordinary differential equations (34-XX) 18 Mechanics of deformable solids (74-XX) 17 Global analysis, analysis on manifolds (58-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Information and communication theory, circuits (94-XX) 11 Systems theory; control (93-XX) 9 Classical thermodynamics, heat transfer (80-XX) 7 Differential geometry (53-XX) 6 Difference and functional equations (39-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Integral transforms, operational calculus (44-XX) 6 Geophysics (86-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of particles and systems (70-XX) 5 Astronomy and astrophysics (85-XX) 4 Statistics (62-XX) 4 Relativity and gravitational theory (83-XX) 3 Special functions (33-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Convex and discrete geometry (52-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX)