Ground state of the time-independent Gross-Pitaevskii equation
Claude M. Dion, Eric Cances
TL;DR
This paper introduces a set of computational tools employing the Optimal Damping Algorithm to efficiently find the ground state solutions of the time-independent Gross-Pitaevskii equation across various dimensions and numerical methods.
Contribution
It provides versatile programs for solving the Gross-Pitaevskii equation with improved convergence, applicable to different trapping potentials and dimensions.
Findings
Fast convergence to ground state achieved
Applicable to 1D, 2D, and 3D cases
Supports spectral and grid-based methods
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.
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