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SUMMARY:Quantum Hall transitions and conformal restriction - Gruzberg\, I 
 (University of Chicago)
DTSTART:20120917T132000Z
DTEND:20120917T140000Z
UID:TALK39818@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A spectacular success in the study of random fractal clusters 
 and their boundaries in critical statistical mechanics systems using Schra
 mm-Loewner Evolutions (SLE) naturally calls for extensions in various dire
 ctions. Can this success be repeated for disordered and/or non-equilibrium
  systems? Naively\, when one thinks about disordered systems and their ave
 rage correlation functions one of the very basic assumptions of SLE\, the 
 so called domain Markov property\, is lost. Also\, in some lattice models 
 of Anderson transitions (the network models) there are no natural clusters
  to consider. Nevertheless\, in this talk I will argue that one can apply 
 the so called conformal restriction\, a notion of stochastic conformal geo
 metry closely related to SLE\, to study the integer quantum Hall transitio
 n and its variants. I will focus on the Chalker-Coddington network model a
 nd will demonstrate that its average transport properties can be mapped to
  a classical problem where the basic objects ar e geometric shapes (loosel
 y speaking\, the current paths) that obey an important restriction propert
 y. At the transition point this allows to use the theory of conformal rest
 riction to derive exact expressions for mean point contact conductances in
  the presence of various non-trivial boundary conditions. \n
LOCATION:Seminar Room 1\, Newton Institute
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