The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates
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Publication:719680
DOI10.1007/S00039-011-0116-9zbMATH Open1242.82036arXiv1008.3811OpenAlexW2024010984MaRDI QIDQ719680
Author name not available (Why is that?)
Publication date: 11 October 2011
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1008.3811
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