Numerical method for evolving the Projected Gross-Pitaevskii equation

TL;DR

This paper introduces a spectral method based on Hermite polynomials for efficiently solving the projected Gross-Pitaevskii equation, enabling accurate simulation of Bose gases in harmonic traps.

Contribution

It presents a novel spectral scheme that precisely enforces mode restrictions in the PGPE, improving the accuracy and efficiency of Bose gas simulations.

Findings

Successfully applied to equilibrium states of Bose gases

Demonstrated accurate non-equilibrium dynamics simulation

Enhanced computational efficiency in mode restriction

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.