Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates
Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Enstein Condensate (BEC), we formally derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the 1 ↔ 2 interactions between the condensate and the excited atoms. The other two describe the 2 ↔ 2 and 1 ↔ 3 interactions between the excited atoms themselves. This is joint work with Yves Pomeau (ENS Paris).