# The linear Boltzmann equation as the low density limit of a random Schrödinger equation

Eng D, Erdös L. 2005. The linear Boltzmann equation as the low density limit of a random Schrödinger equation. Reviews in Mathematical Physics. 17(6), 669–743.

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*Journal Article*|

*Published*

Author

Eng, David;
Erdös, László

^{IST Austria}^{}Abstract

We study the long time evolution of a quantum particle interacting with a random potential in the Boltzmann-Grad low density limit. We prove that the phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation. The Boltzmann collision kernel is given by the full quantum scattering cross-section of the obstacle potential.

Publishing Year

Date Published

2005-07-01

Journal Title

Reviews in Mathematical Physics

Volume

17

Issue

6

Page

669 - 743

IST-REx-ID

### Cite this

Eng D, Erdös L. The linear Boltzmann equation as the low density limit of a random Schrödinger equation.

*Reviews in Mathematical Physics*. 2005;17(6):669-743. doi:10.1142/S0129055X0500242XEng, D., & Erdös, L. (2005). The linear Boltzmann equation as the low density limit of a random Schrödinger equation.

*Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X0500242XEng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.”

*Reviews in Mathematical Physics*. World Scientific Publishing, 2005. https://doi.org/10.1142/S0129055X0500242X.D. Eng and L. Erdös, “The linear Boltzmann equation as the low density limit of a random Schrödinger equation,”

*Reviews in Mathematical Physics*, vol. 17, no. 6. World Scientific Publishing, pp. 669–743, 2005.Eng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.”

*Reviews in Mathematical Physics*, vol. 17, no. 6, World Scientific Publishing, 2005, pp. 669–743, doi:10.1142/S0129055X0500242X.