GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations I: computation of stationary solutions

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

1 IECL - Institut Élie Cartan de Lorraine
2 ALICE - Geometry and Lighting
3 CORIDA - Robust control of infinite dimensional systems and applications

This paper presents GPELab (Gross-Pitaevskii Equation Laboratory), an advanced easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics situations related to Bose-Einstein condensation. The model equation that GPELab solves is the Gross-Pitaevskii equation. The aim of this first part is to present the physical problems and the robust and accurate numerical schemes that are implemented for computing stationary solutions, to show a few computational examples and to explain how the basic GPELab functions work. Problems that can be solved include: 1d, 2d and 3d situations, general potentials, large classes of local and nonlocal nonlinearities, multi-components problems, fast rotating gazes. The toolbox is developed in such a way that other physics applications that require the numerical solution of general Schrödinger-type equations can be considered.GPELab also presents some functionalities to compute the dynamics of Bose-Einstein condensates and to numerically include some stochastic effects.

Mots clés: conjugate normalized gradient flow; stationary states; ground states; numerical simulation; imaginary time; nonlinear Schrödinger equation; Gross-Pitaevskii equation; Bose-Einstein condensates; computational methods; pseudospectral method

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

Xavier Antoine, Romain Duboscq. GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations I: computation of stationary solutions. Computer Physics Communications, 2014, 185 (11), pp.2969-2991. ⟨10.1016/j.cpc.2014.06.026⟩. ⟨hal-01094315⟩