The Boltzmann-Grad limit of the periodic Lorentz gas

Pages 225-298 from Volume 174 (2011), Issue 1 by Jens Marklof, Andreas Strömbergsson

Abstract

We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.

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Keywords
, , ,
DOI
http://doi.org/10.4007/annals.2011.174.1.7
MR
2811599
zbMATH
05960701
Milestones
Received: 4 January 2008
Accepted: 6 May 2010
Published online: 1 July 2011

Authors

Jens Marklof

School of Mathematics
University of Bristol
Bristol BS8 1TW
United Kingdom

Andreas Strömbergsson

Department of Mathematics
Box 480
Uppsala University
SE-75106 Uppsala
Sweden