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

D. Eng, L. Erdös, Reviews in Mathematical Physics 17 (2005) 669–743.

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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

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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/S0129055X0500242X
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. https://doi.org/10.1142/S0129055X0500242X
Eng, David, and László Erdös. “The Linear Boltzmann Equation as the Low Density Limit of a Random Schrödinger Equation.” Reviews in Mathematical Physics 17, no. 6 (2005): 669–743. 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, pp. 669–743, 2005.
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.
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.

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