Microscopic nonequilibrium dynamics of an inhomogeneous Bose gas beyond   the Born approximation
  Using the prescription of the nonequilibrium statistical operator method, we derive a non-Markovian generalization to the kinetic theory described by Walser {\sl et al.} [Phys. Rev. A {\bf 59}, 3878 (1999)]. Quasi-particle damping and effects arising from the finite duration of a collision are introduced to include terms beyond the Born approximation. Such a self-consistent theory is shown to conserve energy to second order in the interaction strength, even in the Markov limit. This kinetic theory is applied to a simple model of a Bose gas confined in a spherical trap to study the full real-time evolution towards equilibrium. A modified form for the damping function, is seen to strongly improve the energy conservation. Based on a linear response calculation, we predict the damping rates and frequencies of the collective excitations. We demonstrate the emergence of differing time scales for damping and equilibration. 
S. G. Bhongale, R. Walser, and M. J. Holland