Coupled dynamics of condensate and non-condensate in the trapped Bose gas

Abstract

Starting from first principles of the statistical mechanics we construct a dynamics of the condensed Bose gas at the nonzero temperatures. In particular, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. Obtained generalized Gross-Pitaevskii equation for condensate include effect of collisions with thermal cloud atoms (non-condensate). The Boltzmann quantum kinetic equation for non-condensate was obtained using Zubarev’s method of nonequilibrium statistical operator. Therefore was obtained a complete dynamics of the condensed Bose gas at the nonzero temperatures.