Wave kinetic description of Bose Einstein condensates

A kinetic approach to cold atoms and Bose-Einstein condensates is explored. This approach is based on the Wigner transformation, which allows for a classical phase space representation of a quantum system. Wave kinetic equations exactly equivalent to the Gross Pitaevskii equation are considered, and various approximations are discussed. In the quasi-classical limit, we obtain the particle number conservation equation. Several different examples of application of this method are given. They include, self-phase modulation of a BE condensate, modulational instability and wakefield generation by a cold atom beam in a thermal background, and kinetic dispersion relation of Bogoliubov oscillations with collisionless Landau damping.