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The stochastic Gross-Pitaevskii equation represents a versatile approach forstudying the dynamics of trapped degenerate ultracold Bose gases in thepresence of large phase and density fluctuations. Following a brief review ofthe original formulation of Stoof, which highlights the benefits of thisapproach and its relation to alternative theories, we present selectedapplications for the dynamics of effectively one-dimensional systems, andbriefly discuss the generalization to two-dimensional systems, highlightingcertain potential pitfalls in their numerical implementations.

The Stochastic Gross-Pitaevskii Equation and some Applications