Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques

TL;DR

This paper reviews phase space techniques based on the Wigner representation for modeling dilute ultra-cold Bose gases, capturing quantum and thermal fluctuations through stochastic equations similar to the Gross-Pitaevskii equation.

Contribution

It develops and discusses c-field methods for zero and finite temperature regimes, providing practical tools for simulating equilibrium and dynamical properties of Bose gases.

Findings

Effective approximation of quantum effects in Bose gases

Numerical methods for implementing stochastic c-field equations

Applications to diverse phenomena in ultra-cold Bose gases

Abstract

We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented.