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

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.

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*Journal Article*|

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Author

Erdös, László

^{IST Austria}^{}; Yau, Horng-TzerAbstract

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

IST-REx-ID

### Cite this

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;2-5Erdös, L., & Yau, H. (2000). Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation.

*Communications on Pure and Applied Mathematics*. Wiley-Blackwell. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5Erdös, László, and Horng Yau. “Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrödinger Equation.”

*Communications on Pure and Applied Mathematics*. Wiley-Blackwell, 2000. 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. Wiley-Blackwell, pp. 667–735, 2000.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.