Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates: A unified framework
Abstract
Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Enstein Condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the 12 interactions between the condensate and the excited atoms. The other two describe the 22 and 13 interactions between the excited atoms themselves.
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