Quantum kinetic theory. III. Quantum kinetic master equation for strongly condensed trapped systems

We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle-number-conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles-nevertheless, the stationary state exhibits the property of off-diagonal long-range order, to the extent that this concept makes sense in a tightly trapped condensate.