# Linear Boltzmann equation as scaling limit of quantum Lorentz gas

Erdös L, Yau H. 1998.Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In: Advances in Differential Equations and Mathematical Physics. Contemporary Mathematics, vol. 217, 137–155.

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DOI

*Book Chapter*|

*Published*|

*English*

Author

Erdös, László

^{ISTA}^{}; Yau, HorngSeries Title

Contemporary Mathematics

Abstract

We study a quantum particle in a random potential in two scaling limits: the low density limit (or Boltzman-Grad) and the weak coupling limit. The low density limit is the quantum analogue of the Lorentz gas. In both cases, the phase space density of the quantum evolution defined through the Wigner transform or the Husimi function converges weakly to a linear Boltz-mann equation with collision kernel given by the quantum scattering cross section.

Publishing Year

Date Published

1998-01-01

Book Title

Advances in Differential Equations and Mathematical Physics

Volume

217

Page

137 - 155

ISSN

IST-REx-ID

### Cite this

Erdös L, Yau H. Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In:

*Advances in Differential Equations and Mathematical Physics*. Vol 217. American Mathematical Society; 1998:137-155. doi:10.1090/conm/217Erdös, L., & Yau, H. (1998). Linear Boltzmann equation as scaling limit of quantum Lorentz gas. In

*Advances in Differential Equations and Mathematical Physics*(Vol. 217, pp. 137–155). American Mathematical Society. https://doi.org/10.1090/conm/217Erdös, László, and Horng Yau. “Linear Boltzmann Equation as Scaling Limit of Quantum Lorentz Gas.” In

*Advances in Differential Equations and Mathematical Physics*, 217:137–55. American Mathematical Society, 1998. https://doi.org/10.1090/conm/217.L. Erdös and H. Yau, “Linear Boltzmann equation as scaling limit of quantum Lorentz gas,” in

*Advances in Differential Equations and Mathematical Physics*, vol. 217, American Mathematical Society, 1998, pp. 137–155.Erdös, László, and Horng Yau. “Linear Boltzmann Equation as Scaling Limit of Quantum Lorentz Gas.”

*Advances in Differential Equations and Mathematical Physics*, vol. 217, American Mathematical Society, 1998, pp. 137–55, doi:10.1090/conm/217.