C-Field Methods for Non-Equilibrium Bose Gases

TL;DR

This paper reviews c-field simulation methods for non-equilibrium Bose gases, detailing three approaches—PGPE, SPGPE, and TWPGPE—and their regimes of validity, with applications to vortex formation in condensates.

Contribution

It provides a comprehensive comparison of three c-field methods for simulating non-equilibrium Bose gases, clarifying their regimes and relationships.

Findings

SPGPE effectively models vortex formation dynamics.

Different methods are valid in specific temperature regimes.

The paper clarifies the regimes of applicability for each approach.

Abstract

We review c-field methods for simulating the non-equilibrium dynamics of degenerate Bose gases beyond the mean-field Gross-Pitaevskii approximation. We describe three separate approaches that utilise similar numerical methods, but have distinct regimes of validity. Systems at finite temperature can be treated with either the closed-system projected Gross-Pitaevskii equation (PGPE), or the open-system stochastic projected Gross-Pitaevskii equation (SPGPE). These are both applicable in quantum degenerate regimes in which thermal fluctuations are significant. At low or zero temperature, the truncated Wigner projected Gross-Pitaevskii equation (TWPGPE) allows for the simulation of systems in which spontaneous collision processes seeded by quantum fluctuations are important. We describe the regimes of validity of each of these methods, and discuss their relationships to one another, and to other simulation techniques for the dynamics of Bose gases. The utility of the SPGPE formalism in modelling non-equilibrium Bose gases is illustrated by its application to the dynamics of spontaneous vortex formation in the growth of a Bose-Einstein condensate.