Quantum Boltzmann dynamics and bosonized particle-hole interactions in fermion gases
Abstract
In this paper, we study a cold gas of N 1 weakly interacting fermions. We describe the time evolution of states that are perturbations of the Fermi ball, and analyze the dynamics in particle-hole variables. Our main result states that, for small values of the coupling constant and for appropriate initial data, the effective dynamics of the momentum distribution is determined by a discrete collision operator of quantum Boltzmann form.
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