GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: dynamics and stochastic simulations

Xavier Antoine (1, 2) , Romain Duboscq (3)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 IMT - Institut de Mathématiques de Toulouse UMR5219

GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross–Pitaevskii equations that arise in the physics of Bose–Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross–Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.

Mots clés: Stochastic dynamics; Nonlinear dynamics; Gross–Pitaevskii equation; Numerical simulation; Bose–Einstein condensates; Computational schemes; Nonlinear Schrödinger equation

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Gaz Quantiques [cond-mat.quant-gas]; Physique mathématique [math-ph]

Xavier Antoine, Romain Duboscq. GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: dynamics and stochastic simulations. Computer Physics Communications, 2015, 193, pp.95-117. ⟨10.1016/j.cpc.2015.03.012⟩. ⟨hal-01095568⟩