Speaker:  Michael Hott, U of Minnesota

Title: Emergence of renormalized Hartree-Fock-Bogoliubov and Quantum-Boltzmann equations in an interacting Bose gas

Abstract:  The study of kinetic equations describing collisions between a BEC and the surrounding normal fluid go back to Kirkpatrick and Dorfmann ’83, ’85 and Eckern ’84. Ever since, this subject has attracted a lot of attention as it relates to condensation. In this context, mathematicians have studied the quartic quantum Boltzmann equation in the presence of a BEC. In this talk, we will discuss some of the progress made on the PDE level of the quantum Boltzmann equation. Then, we will focus on the validity of the kinetic equations. We will describe the crucial scale separations needed to extract a Boltzmann equation from the quantum dynamics. Moreover, we will see how the interference of sound waves can produce some surprising effects if a Bose gas is trapped in a volume of unit size. This is based on joint work with Thomas Chen.