Linear Boltzmann equation as the weak coupling limit of the random SchrÃ¶dinger equation
We study the long 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 the solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approximation of the quantum scattering cross section.
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233 - 242
233 - 242
World Scientific Publishing