Publication: Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
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2000
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Wiley-Blackwell
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Erdős, László, and Horng‐Tzer Yau. "Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation." Communications on Pure and Applied Mathematics 53, no. 6 (2000): 667-735.
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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