Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap
Statistical Mechanics
2016-08-31 v3
Abstract
By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth order algorithms are possible only with the use of {\it forward}, positive time step factorization schemes. These fourth order algorithms converge at time-step sizes an order-of-magnitude larger than conventional second order algorithms. Our use of time-dependent factorization schemes provides a systematic way of devising algorithms for solving this type of nonlinear equations.
Keywords
Cite
@article{arxiv.cond-mat/0504270,
title = {Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap},
author = {Siu A. Chin and Eckhard Krotscheck},
journal= {arXiv preprint arXiv:cond-mat/0504270},
year = {2016}
}
Comments
14 pages with 3 figures, revised figures with the use of the Lambert W-function for doing the self-consistent iterations. Published version