Quantum Kinetic Theory of BEC Lattice Gas:Boltzmann Equations from 2PI-CTP Effective Action

TL;DR

This paper derives quantum kinetic equations for a Bose-Einstein condensate in an optical lattice using the 2PI-CTP effective action, connecting microscopic theory to observable dynamics.

Contribution

It introduces a method to derive quantum kinetic equations from the 2PI-CTP effective action for the Bose-Hubbard model, linking microscopic quantum field theory to kinetic descriptions.

Findings

Reproduces Beliaev's second-order self-energy corrections

Derives Kadanoff-Baym equations from 2PI-CTP effective action

Establishes a framework for quantum kinetic theory of many-atom systems

Abstract

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.