The stochastic projected Gross-Pitaevskii equation

TL;DR

This paper presents the first full implementation of the stochastic projected Gross-Pitaevskii equation for a 3D trapped Bose gas at finite temperature, including number-conserving scattering processes, and analyzes their impact on system dynamics.

Contribution

It introduces a comprehensive numerical implementation of scattering processes in the stochastic projected Gross-Pitaevskii equation, extending previous models that only included growth.

Findings

Scattering processes can dominate over growth in non-equilibrium regimes.

Scattering leads to rapid thermalization without significant condensate depletion.

The energy transfer via scattering is highly coherent.

Abstract

We have achieved the first full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only included growth processes, by implementing number-conserving scattering processes. We evaluate an analytic expression for the coefficient of the scattering term and compare it to that of the growth term in the experimental regime, showing the two coefficients are comparable in size. We give an overview of the numerical implementation of the deterministic and stochastic terms for the scattering process, and use simulations of a condensate excited into a large amplitude breathing mode oscillation to characterize the importance of scattering and growth processes in an experimentally accessible regime. We find that in such non-equilibrium regimes the scattering can dominate over the growth, leading to qualitatively different system dynamics. In particular, the scattering causes the system to rapidly reach thermal equilibrium without greatly depleting the condensate, suggesting that it provides a highly coherent energy transfer mechanism.