The Stochastic Gross-Pitaevskii Equation and some Applications

TL;DR

This paper reviews the stochastic Gross-Pitaevskii equation, emphasizing its usefulness for modeling ultracold Bose gases with large fluctuations, and discusses applications and numerical challenges in 1D and 2D systems.

Contribution

It provides a concise review of the stochastic Gross-Pitaevskii equation and explores its applications to low-dimensional Bose gases, including potential numerical pitfalls.

Findings

Demonstrates the equation's effectiveness in modeling 1D Bose gases.

Discusses generalization to 2D systems and associated challenges.

Highlights the relation to alternative theoretical approaches.

Abstract

The stochastic Gross-Pitaevskii equation represents a versatile approach for studying the dynamics of trapped degenerate ultracold Bose gases in the presence of large phase and density fluctuations. Following a brief review of the original formulation of Stoof, which highlights the benefits of this approach and its relation to alternative theories, we present selected applications for the dynamics of effectively one-dimensional systems, and briefly discuss the generalization to two-dimensional systems, highlighting certain potential pitfalls in their numerical implementations.