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SUMMARY:Kinetic transport in crystals and quasicrystals - Marklof\, J (Uni
 versity of Bristol)
DTSTART:20150326T100000Z
DTEND:20150326T110000Z
UID:TALK58607@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The Lorentz gas is one of the simplest\, most widely used mode
 ls to study the transport properties of rarified gases in matter. It descr
 ibes the dynamics of a cloud of non-interacting point particles in an infi
 nite array of fixed spherical scatterers. More than one hundred years afte
 r its conception\, it is still a major challenge to understand the nature 
 of the kinetic transport equation that governs the macroscopic particle dy
 namics in the limit of low scatterer density (the Boltzmann-Grad limit). L
 orentz suggested that this equation should be the linear Boltzmann equatio
 n. This was confirmed in three celebrated papers by Gallavotti\, Spohn\, a
 nd Boldrighini\, Bunimovich and Sinai\, under the assumption that the dist
 ribution of scatterers is sufficiently disordered. In the case of strongly
  correlated scatterer configurations (such as crystals or quasicrystals)\,
  we now understand why the linear Boltzmann equation fails and what to sub
 stitute it with. A particularly striking featur e of the periodic Lorentz 
 gas is a heavy tail for the distribution of free path lengths\, with a div
 erging second moment\, and superdiffusive transport in the limit of large 
 times.\n\nJoint work with A. Strombergsson and B. Toth.\n
LOCATION:Seminar Room 1\, Newton Institute
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