Fortran programs for the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap

Abstract
Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross–Pitaevskii (GP) equation describing the properties of Bose–Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank–Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimens...

Title of program: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial
Catalogue Id: AEDU_v1_0

Nature of problem
These programs are designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one, two or three space dimensions with a harmonic, circularly-symmetric, spherically-symmetric, axially-symmetric or anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate.

Versions of this program held in the CPC repository in Mendeley Data
AEDU_v1_0; (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial; 10.1016/j.cpc.2009.04.015
AEDU_v2_0; GP-SCL package, consisting of: (i) imagtime1d, (ii) imagtime2d, (iii) imagtime2d-th, (iv) imagtimecir, (v) imagtime3d, (vi) imagtime3d-th, (vii) imagtimeaxial, (viii) imagtimeaxial-th, (ix) imagtimesph, (x) realtime1d, (xi) realtime2d, (xii) realtime2d-th, (xiii) realtimecir, (xiv) realtime3d, (xv) realtime3d-th, (xvi) realtimeaxial, (xvii) realtimeaxial-th, (xviii) realtimesph; 10.1016/j.cpc.2012.03.022
AEDU_v3_0; GP-SCL-HYB package, consisting of: (i) imagtime3d-hyb, (ii) realtime3d-hyb.; 10.1016/j.cpc.2015.12.006
AEDU_v4_0; BEC-GP-OMP package, consisting of: (i) imag1d, (ii) imag2d, (iii) imag3d, (iv) imagaxi, (v) imagcir, (vi) imagsph, (vii) real1d, (viii) real2d, (ix) real3d, (x) realaxi, (xi) realcir, (xii) realsph.; 10.1016/j.cpc.2016.03.015

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要
本文针对描述极低温下玻色-爱因斯坦凝聚态（Bose–Einstein condensate, BEC）特性的含时Gross–Pitaevskii（GP）方程的定态与非定态解，开发了简易数值算法。具体而言，我们研究了基于分裂步Crank–Nicolson方法的实时间与虚时间传播算法。针对单空间变量形式的GP方程，我们分别考虑了一维、二维圆对称以及三维……

程序名称：(i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial
程序馆藏编号：AEDU_v1_0

问题性质
本系列程序用于求解一维、二维或三维空间维度下，带有简谐、圆对称、球对称、轴对称或各向异性势阱的含时Gross–Pitaevskii非线性偏微分方程。Gross–Pitaevskii方程用于描述稀薄囚禁玻色-爱因斯坦凝聚态的物理特性。

本程序在Mendeley数据的CPC数据库中的版本信息如下：
AEDU_v1_0；(i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial；10.1016/j.cpc.2009.04.015
AEDU_v2_0；GP-SCL程序包，包含：(i) imagtime1d, (ii) imagetime2d, (iii) imagtime2d-th, (iv) imagtimecir, (v) imagtime3d, (vi) imagtime3d-th, (vii) imagtimeaxial, (viii) imagtimeaxial-th, (ix) imagtimesph, (x) realtime1d, (xi) realtime2d, (xii) realtime2d-th, (xiii) realtimecir, (xiv) realtime3d, (xv) realtime3d-th, (xvi) realtimeaxial, (xvii) realtimeaxial-th, (xviii) realtimesph；10.1016/j.cpc.2012.03.022
AEDU_v3_0；GP-SCL-HYB程序包，包含：(i) imagtime3d-hyb, (ii) realtime3d-hyb；10.1016/j.cpc.2015.12.006
AEDU_v4_0；BEC-GP-OMP程序包，包含：(i) imag1d, (ii) imag2d, (iii) imag3d, (iv) imagaxi, (v) imagcir, (vi) imagsph, (vii) real1d, (viii) real2d, (ix) real3d, (x) realaxi, (xi) realcir, (xii) realsph；10.1016/j.cpc.2016.03.015

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018年）