Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation

L. Erdös, H. Yau, Communications on Pure and Applied Mathematics 53 (2000) 667–735.

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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.
Publishing Year
Date Published
2000-06-01
Journal Title
Communications on Pure and Applied Mathematics
Volume
53
Issue
6
Page
667 - 735
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Erdös L, Yau H. Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Communications on Pure and Applied Mathematics. 2000;53(6):667-735. doi:10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
Erdös, L., & Yau, H. (2000). Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Communications on Pure and Applied Mathematics, 53(6), 667–735. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
Erdös, László, and Horng 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. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5.
L. Erdös and H. Yau, “Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation,” Communications on Pure and Applied Mathematics, vol. 53, no. 6, pp. 667–735, 2000.
Erdös L, Yau H. 2000. Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Communications on Pure and Applied Mathematics. 53(6), 667–735.
Erdös, László, and Horng Yau. “Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrödinger Equation.” Communications on Pure and Applied Mathematics, vol. 53, no. 6, Wiley-Blackwell, 2000, pp. 667–735, doi:10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5.

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