THE LINEAR BOLTZMANN EQUATION AS THE LOW DENSITY LIMIT OF A RANDOM SCHRÖDINGER EQUATION-Reference-Cited by-同舟云学术

THE LINEAR BOLTZMANN EQUATION AS THE LOW DENSITY LIMIT OF A RANDOM SCHRÖDINGER EQUATION

Published:2005-07 Issue:06 Volume:17 Page:669-743
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

ENG DAVID¹,ERDŐS LÁSZLÓ²

Affiliation:

1. Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA

2. Institute of Mathematics, University of Munich, Theresienstr. 39, D-80333 Munich, Germany

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X0500242X

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