Numerical method for evolving the Projected Gross-Pitaevskii equation
Abstract
In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy classical region of the system. We present a scheme, using a Hermite-polynomial based spectral representation, that precisely implements this mode restriction and allows an efficient and accurate solution of the PGPE. We show equilibrium and non-equilibrium results from the application of the PGPE to an anisotropic trapped three-dimensional Bose gas.
Cite
@article{arxiv.0803.3664,
title = {Numerical method for evolving the Projected Gross-Pitaevskii equation},
author = {P. B. Blakie},
journal= {arXiv preprint arXiv:0803.3664},
year = {2008}
}
Comments
12 pages, 5 figures. To appear in Phys. Rev. E. Convergence results added, a few minor changes made and typos fixed