Ground state of the time-independent Gross–Pitaevskii equation

Abstract
We present a suite of programs to determine the ground state of the time-independent Gross-Pitaevskii equation, used in the simulation of Bose-Einstein condensates. The calculation is based on the Optimal Damping Algorithm, ensuring a fast convergence to the true ground state. Versions are given for the one-, two-, and three-dimensional equation, using either a spectral method, well suited for harmonic trapping potentials, or a spatial grid.

Title of program: GPODA
Catalogue Id: ADZN_v1_0

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 on ...

Versions of this program held in the CPC repository in Mendeley Data
ADZN_v1_0; GPODA; 10.1016/j.cpc.2007.04.007

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本文提出一套程序套件，用于求解与时间无关的格罗斯-皮塔耶夫斯基方程（Gross-Pitaevskii equation, GPE）的基态，该方程广泛应用于玻色-爱因斯坦凝聚体（Bose-Einstein condensates, BEC）的数值模拟。本计算基于最优阻尼算法（Optimal Damping Algorithm），可确保快速收敛至真实基态。程序提供一维、二维及三维形式的方程求解版本，可采用适配简谐束缚势（harmonic trapping potentials）的谱方法（spectral method），或空间网格法两种实现方案。

程序名称：GPODA
目录编号：ADZN_v1_0

问题本质
在平均场近似框架下，玻色-爱因斯坦凝聚体（BEC）的序参量（或称波函数）可通过格罗斯-皮塔耶夫斯基方程（GPE）[1]求解。GPE是一类类非线性薛定谔方程，本文所涉版本包含束缚势项。通过求解与时间无关的GPE的基态，即可得到BEC的定态，即能使系统能量最小化的序参量。除标准的三维GPE外，强束缚势还可导出有效的二维甚至一维……

该程序收录于Mendeley数据的CPC程序库中，对应条目为ADZN_v1_0；GPODA；DOI: 10.1016/j.cpc.2007.04.007

本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）