On quantum Boltzmann fluctuation dynamics at the presence of a Bose-Einstein condensate

The derivation of a Boltzmann equation from first principles has been a long-standing problem. In a seminal work, Lanford showed the validity of a classical Boltzmann equation for an ideal dilute hard-sphere gas for times up to one third of the collision time. A lot of progress has been made ever since. I will explain how a cubic quantum Boltzmann equation arises within the fluctuation dynamics of a Bose-Einstein condensate, starting with the van Neumann equation for an ideal Boson gas.