Title :

Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations

Author(s) :

Antoine, Xavier [Auteur]
Institut Élie Cartan de Lorraine [IECL]
Robust control of infinite dimensional systems and applications [CORIDA]
Bao, Weizhu [Auteur]
Department of Mathematics [Singapore]
Besse, Christophe [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Computer Physics Communications

Pages :

2621-2633

Publisher :

Elsevier

Publication date :

2013

ISSN :

0010-4655

English keyword(s) :

Gross-Pitaevskii equation
absorbing boundary condition
Crank-Nicolson finite difference method
time-splitting spectral method
nonlinear Schrödinger equation
Bose-Einstein condensation

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Physique mathématique [math-ph]
Physique [physics]/Matière Condensée [cond-mat]/Gaz Quantiques [cond-mat.quant-gas]
Physique [physics]/Physique Quantique [quant-ph]

English abstract : [en]

In this paper, we begin with the nonlinear Schrödinger/Gross-Pitaevskii equation (NLSE/GPE) for modeling Bose-Einstein condensation (BEC) and nonlinear optics, and discuss their dynamical properties ranging from time ...
Show more >In this paper, we begin with the nonlinear Schrödinger/Gross-Pitaevskii equation (NLSE/GPE) for modeling Bose-Einstein condensation (BEC) and nonlinear optics, and discuss their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, dispersive relation to soliton solutions. Then, we review and compare different numerical methods for solving the NLSE/GPE including finite difference time domain methods and time-splitting spectral method, and discuss different absorbing boundary conditions. In addition, these numerical methods are extendedto the NLSE/GPE with damping terms and/or an angular momentum rotation term as well as coupled NLSEs/GPEs. Finally, applications to simulate a quantized vortex lattice dynamics in a rotating BEC are reported.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Simulation numérique avancée pour les condensats de Bose-Einstein : Modèles numériques déterministes et stochastiques, Calcul haute performance, Simulation d'expériences physiques

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL