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Manuscript Title: Ground state of the time-independent Gross-Pitaevskii equation
Authors: Claude M. Dion, Eric Cancès
Program title: GPODA
Catalogue identifier: ADZN_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 177(2007)787
Programming language: Fortran 90.
Computer: ANY (Compilers under which the program has been tested: Absoft Pro Fortran, The Portland Group Fortran 90/95 compiler, Intel Fortran Compiler).
Operating system: Mac OS X, Linux.
RAM: From < 1 MB in 1D to ~ 102 MB for a large 3D grid
Keywords: Gross-Pitaevskii equation, Bose-Einstein condensate, Optimal Damping Algorithm.
PACS: 03.75.Hh, 03.65.Ge, 02.60.Pn, 02.70.-c.
Classification: 2.7, 4.9.

External routines: LAPACK, BLAS, DFFTPACK

Nature of problem:
The order parameter (or wave function) of a Bose-Einstein condensate (BEC) is obtained, in a mean field approximation, by the Gross-Pitaevskii equation (GPE)[1]. The GPE is a nonlinear Schrödinger-like equation, including here a confining potential. The stationary state of a BEC is obtained by finding the ground state of the time-independent GPE, ie, the order parameter that minimizes the energy. In addition to the standard three-dimensional GPE, tight traps can lead to effective two- or even one-dimensional BECs, so the 2D and 1D GPEs are also considered.

Solution method:
The ground state of the time-independent of the GPE is calculated using the Optimal Damping Algorithm [2]. Two sets of programs are given, using either a spectral representation of the order parameter [3], suitable for a (quasi) harmonic trapping potential, or by discretizing the order parameter on a spatial grid.

Running time:
From seconds for in 1D to a few hours for large 3D grids.

References:
[1] F. Dalfovo, S. Giorgini, L. P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71 (1999) 463.
[2] E. Cancès, C. Le Bris, Int. J. Quantum Chem. 79 (2000) 82.
[3] C. M. Dion, E. Cancès, Phys. Rev. E 67 (2003) 046706.