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SUMMARY: Kinetic theory for the low-density Lorentz gas - Jens Marklof (Br
 istol)
DTSTART:20191203T140000Z
DTEND:20191203T150000Z
UID:TALK131485@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The Lorentz gas is one of the simplest and most widely-studied
  models\nfor particle transport in matter. It describes a cloud of\nnon-in
 teracting gas particles in an infinitely extended array of\nidentical sphe
 rical scatterers\, whose radii are small compared to their\nmean separatio
 n. The model was introduced by Lorentz in 1905 who\,\nfollowing the pionee
 ring ideas of Maxwell and Boltzmann\, postulated that\nits macroscopic tra
 nsport properties should be governed by a linear\nBoltzmann equation. A ri
 gorous derivation of the linear Boltzmann\nequation from the underlying pa
 rticle dynamics was given\, for random\nscatterer configurations\, in thre
 e seminal papers by Gallavotti\, Spohn\nand Boldrighini-Bunimovich-Sinai. 
 The objective of this lecture is to\ndevelop an approach for a large class
  of deterministic scatterer\nconfigurations\, including various types of q
 uasicrystals. We prove the\nconvergence of the particle dynamics to transp
 ort processes that are in\ngeneral (depending on the scatterer configurati
 on) not described by the\nlinear Boltzmann equation. This was previously u
 nderstood only in the\ncase of the periodic Lorentz gas through work of Ca
 glioti-Golse and\nMarklof-Strombergsson. Our results extend beyond the cla
 ssical Lorentz\ngas with hard sphere scatterers\, and in particular hold f
 or general\nclasses of spherically symmetric finite-range potentials. We e
 mploy a\nrescaling technique that randomises the point configuration given
  by the\nscatterers' centers. The limiting transport process is then expre
 ssed in\nterms of a point process that arises as the limit of the randomis
 ed\npoint configuration under a certain volume-preserving one-parameter\nl
 inear group action.\nJoint work with Andreas Strombergsson (Uppsala)\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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