Quantum Kinetic Theory of BEC Lattice Gas:Boltzmann Equations from   2PI-CTP Effective Action
  We continue our earlier work [Ana Maria Rey, B. L. Hu, Esteban Calzetta, Albert Roura and Charles W. Clark, Phys. Rev. A 69, 033610 (2004)] on the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical lattice. From the two-particle irreducible (2PI) closed-time-path (CTP) effective action for the Bose- Hubbard Hamiltonian, we show how to obtain the Kadanoff-Baym equations of quantum kinetic theory. Using the quasiparticle approximation, we show that the local equilibrium solutions of these equations reproduce the second- order corrections to the self-energy originally derived by Beliaev. This work paves the way for the use of effective action methods in the derivation of quantum kinetic theory of many atom systems. 
Ana Maria Rey, B. L. Hu, Esteban Calzetta and Charles W. Clark