GSGPEs: A MATLAB code for computing the ground state of systems of Gross-Pitaevskii equations

Abstract GSGPEs is a Matlab/GNU Octave suite of programs for the computation of the ground state of systems of Gross–Pitaevskii equations. It can compute the ground state in the defocusing case, for any number of equations with harmonic or quasi-harmonic trapping potentials, in spatial dimension one, two or three. The computation is based on a spectral decomposition of the solution into Hermite functions and direct minimization of the energy functional through a Newton-like method with an approximate line-search strategy. Program summary Program title: GSGPEs Catalogue identifier: AENT_v1_0 Program summary URL : http://cpc.cs.qub.ac.uk/summaries/AENT_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1417 No. of bytes in distributed program, including test data, etc.: 13673 Distribution format: tar.gz Programming language: Matlab/GNU Octave. Computer: Any supporting Matlab/GNU Octave. Operating system: Any supporting Matlab/GNU Octave. RAM: About 100 MB for a single three-dimensional equation (test run output). Classification: 2.7, 4.9. Nature of problem: A system of Gross–Pitaevskii Equations (GPEs) is used to mathematically model a Bose–Einstein Condensate (BEC) for a mixture of different interacting atomic species. The equations can be used both to compute the ground state solution (i.e., the stationary order parameter that minimizes the energy functional) and to simulate the dynamics. For particular shapes of the traps, three-dimensional BECs can be also simulated by lower dimensional GPEs. Solution method: The ground state of a system of Gross–Pitaevskii equations is computed through a spectral decomposition into Hermite functions and the direct minimization of the energy functional. Running time: About 30 seconds for a single three-dimensional equation with d.o.f. 40 for each spatial direction (test run output).