The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit

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Abstract

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term c = 2-3 ln 2+27ζ(3)/2Π2 in the asymptotic formula h(T) = -2 ln ε +c+o(1) of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.

Original languageEnglish (US)
Pages (from-to)425-471
Number of pages47
JournalCommunications in Mathematical Physics
Volume269
Issue number2
DOIs
StatePublished - Jan 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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