Fortran and C programs for the timedependent dipolar GrossPitaevskii equation in an anisotropic trap
Abstract
Many of the static and dynamic properties of an atomic BoseEinstein condensate (BEC) are usually studied by solving the meanfield GrossPitaevskii (GP) equation, which is a nonlinear partial differential equation for shortrange atomic interaction. More recently, BEC of atoms with longrange dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integrodifferential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and nonstationary solutions of the full threedimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one (1D) and twodimensional (2D) GP equations satisfied by cigar and diskshaped dipolar BECs. We employ the splitstep CrankNicolson method with real and imaginarytime propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and nonstationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x y and x z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, rootmeansquare sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and ThomasFermi approximations.
 Publication:

Computer Physics Communications
 Pub Date:
 October 2015
 DOI:
 10.1016/j.cpc.2015.03.024
 arXiv:
 arXiv:1506.03283
 Bibcode:
 2015CoPhC.195..117K
 Keywords:

 BoseEinstein condensate;
 GrossPitaevskii equation;
 Splitstep CrankNicolson scheme;
 Real and imaginarytime propagation;
 Fortran and C programs;
 Dipolar atoms;
 Condensed Matter  Quantum Gases;
 Mathematical Physics;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Physics  Computational Physics
 EPrint:
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