The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates

J Marklof, A Strombergsson

Research output: Contribution to journalArticle (Academic Journal)peer-review

20 Citations (Scopus)

Abstract

The dynamics of a point particle in a periodic array of spherical scatterers converges, in the limit of small scatterer size, to a random flight process, whose paths are piecewise linear curves generated by a Markov process with memory two. The corresponding transport equation is distinctly different from the linear Boltzmann equation observed in the case of a random configuration of scatterers. In the present paper we provide asymptotic estimates for the transition probabilities of this Markov process. Our results in particular sharpen previous upper and lower bounds on the distribution of free path lengths obtained by Bourgain, Golse and Wennberg.
Translated title of the contributionThe periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates
Original languageEnglish
Pages (from-to)560 - 647
Number of pages88
JournalGeometric and Functional Analysis
Volume21
Issue number3
DOIs
Publication statusPublished - Jun 2011

Bibliographical note

Publisher: Birkhauser

Fingerprint Dive into the research topics of 'The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates'. Together they form a unique fingerprint.

Cite this