Stochastic Gross-Pitaevsky Equation for BEC via Coarse-Grained Effective Action

TL;DR

This paper derives a new stochastic Gross-Pitaevsky equation for Bose-Einstein condensates at zero temperature, incorporating non-condensate effects as stochastic sources using a functional integral approach.

Contribution

It introduces a novel derivation of stochastic GPEs using the coarse-grained effective action, accounting for back-reaction and nonlocal dissipation in BEC dynamics.

Findings

Derived Langevin equations with nonlocal dissipation

Incorporated colored and multiplicative noise effects

Provides a self-consistent stochastic description of BEC dynamics

Abstract

We sketch the major steps in a functional integral derivation of a new set of Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate modes incorporated as stochastic sources. The closed-time-path (CTP) coarse-grained effective action (CGEA) or the equivalent influence functional method is particularly suitable because it can account for the full back-reaction of the noncondensate modes on the condensate dynamics self-consistently. The Langevin equations derived here containing nonlocal dissipation together with colored and multiplicative noises are useful for a stochastic (as distinguished from say, a kinetic) description of the nonequilibrium dynamics of a BEC. This short paper contains original research results not yet published anywhere.