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

Understand

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.