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

Erdös L. 1999. Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation. QMath: Mathematical Results in Quantum Physics, Operator Theory: Advances and Applications, vol. 108, 233–242.

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Operator Theory: Advances and Applications

Abstract

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.

Publishing Year

Date Published

1999-01-01

Volume

108

Page

233 - 242

Conference

QMath: Mathematical Results in Quantum Physics

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Erdös L. Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation. In: Vol 108. World Scientific Publishing; 1999:233-242. doi:10.1007/978-3-0348-8745-8_20

Erdös, L. (1999). Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation (Vol. 108, pp. 233–242). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1007/978-3-0348-8745-8_20

Erdös, László. “Linear Boltzmann Equation as the Weak Coupling Limit of the Random Schrödinger Equation,” 108:233–42. World Scientific Publishing, 1999. https://doi.org/10.1007/978-3-0348-8745-8_20.

L. Erdös, “Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation,” presented at the QMath: Mathematical Results in Quantum Physics, 1999, vol. 108, pp. 233–242.

Erdös, László.

*Linear Boltzmann Equation as the Weak Coupling Limit of the Random Schrödinger Equation*. Vol. 108, World Scientific Publishing, 1999, pp. 233–42, doi:10.1007/978-3-0348-8745-8_20.