Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-09-09
Advances in Physics, 57, 363 (2008)
Physics
Condensed Matter
Statistical Mechanics
110 pages, 32 figures. Updated to address referee comments. To appear in Advances in Physics
Scientific paper
10.1080/00018730802564254
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.
Ballagh Robert J.
Blakie Blair P.
Bradley Alexander S.
Davis Mark J.
Gardiner C. W.
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