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SUMMARY:Kinetic theory for the low-density Lorentz gas (Common session wit
 h Probability Seminar) - Jens Marklof\, University of Bristol 
DTSTART:20191203T140000Z
DTEND:20191203T150000Z
UID:TALK130969@talks.cam.ac.uk
CONTACT:Jessica Guerand
DESCRIPTION: Joint work with Andreas Strombergsson (Uppsala)\n\nThe Lorent
 z gas is one of the simplest and most widely-studied models for particle t
 ransport in matter. It describes a cloud of non-interacting gas particles 
 in an infinitely extended array of identical spherical scatterers\, whose 
 radii are small compared to their mean separation. The model was introduce
 d by Lorentz in 1905 who\, following the pioneering ideas of Maxwell and B
 oltzmann\, postulated that its macroscopic transport properties should be 
 governed by a linear Boltzmann equation. A rigorous derivation of the line
 ar Boltzmann equation from the underlying particle dynamics was given\, fo
 r random scatterer configurations\, in three seminal papers by Gallavotti\
 , Spohn and Boldrighini-Bunimovich-Sinai. The objective of this lecture is
  to develop an approach for a large class of deterministic scatterer confi
 gurations\, including various types of quasicrystals. We prove the converg
 ence of the particle dynamics to transport processes that are in general (
 depending on the scatterer configuration) not described by the linear Bolt
 zmann equation. This was previously understood only in the case of the per
 iodic Lorentz gas through work of Caglioti-Golse and Marklof-Strombergsson
 . Our results extend beyond the classical Lorentz gas with hard sphere sca
 tterers\, and in particular hold for general classes of spherically symmet
 ric finite-range potentials. We employ a rescaling technique that randomis
 es the point configuration given by the scatterers' centers. The limiting 
 transport process is then expressed in terms of a point process that arise
 s as the limit of the randomised point configuration under a certain volum
 e-preserving one-parameter linear group action.
LOCATION:CMS\, MR12
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