Collisionless dynamics of the condensate predicted in the random phase approximation

From the microscopic theory, we derive a number conserving quantum kinetic equation, for a dilute Bose gas valid at any temperature, in which the binary collisions between the quasi-particles are mediated by the Bogoliubov collective excitations. This different approach starts from the many-body Hamiltonian of a Boson gas and uses, in an appropriate way, the generalized random phase approximation. As a result, the collision term of the kinetic equation contains higher order contributions in the expansion in the interaction parameter. The major interest of this particular mechanism is that, in a regime where the condensate is stable, the collision process between condensed and noncondensed particles is totally blocked due to a total annihilation of the mutual interaction potential induced by the condensate itself. As a consequence, the condensate is not constrained to relax and can be superfluid. Furthermore, a Boltzmann-like H-theorem for the entropy exists for this equation and allows to distinguish between dissipative and nondissipative phenomena (like vortices). We also illustrate the analogy between this approach and the kinetic theory for a plasma, in which the collective excitations correspond precisely to a plasmon. The spectrum of these excitations and their damping are exactly the ones obtained from the gapless and conserving equilibrium dielectric formalism developed in Fliesser et al. [Phys. Rev. A 64 (2001) 013609]. Finally, we recover the Bogoliubov results for the ground state energy and the particle momentum distribution. This work contains more details of the summary presented in Navez [J. Low Temp. Phys., 138 (2005) 705–710].