We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes.
Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation
Shock problem for MKdV equation: Long time Dynamics of the Step-like initial data
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field
