On the quantum Boltzmann equation - Erdös, László; Salmhofer, Manfred; Yau, Horng (Journal of Statistical Physics, 2004)
We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrödinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property called restricted quasifreeness in the weak coupling limit at any later time. By definition, a state is called restricted quasifree if the four-point and the eight-point functions of the state factorize in the same manner as in a quasifree state.
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