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

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

2010-08-23

arxiv.org/abs/1008.3811v2

Physics

Mathematical Physics

LaTeX, 71 pages; added arXiv identifier for the reference [29]

Scientific paper

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.

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