Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation
L. Erdos, H. -T. Yau
Abstract
We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approximation of the quantum differential scattering cross section.
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