The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates
2011 (English)In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 21, no 3, 560-647 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2011. Vol. 21, no 3, 560-647 p.
Lorentz gas, Boltzmann-Grad limit, linear Boltzmann equation, lattice points in convex sets
IdentifiersURN: urn:nbn:se:uu:diva-140259DOI: 10.1007/s00039-011-0116-9ISI: 000291752000003OAI: oai:DiVA.org:uu-140259DiVA: diva2:383322