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SUMMARY:The free Bose gas and permutations of integers - Thomas Richthamme
 r (Munich)
DTSTART:20130115T163000Z
DTEND:20130115T173000Z
UID:TALK40510@talks.cam.ac.uk
CONTACT:12974
DESCRIPTION:Using Feynman's representation\, the equilibrium state of the 
 Bose gas can be described in terms of a probabilistic model\, similar to m
 odels from non-quantum statistical mechanics. In this model a particle con
 figuration is characterized by the positions of the particles in combinati
 on with a permutation of the particles. The natural mathematical\nframewor
 k for such a particle model is an infinite volume description\, but in the
  case of\nthe Bose gas model this infinite volume description is still mis
 sing: The main difficulty here is to incorporate the particle permutations
  into the model.\n\nIn order to show how to overcome this difficulty we co
 nsider a toy model\, where the particle positions are fixed at the vertice
 s of the integer lattice. We introduce an infinite volume description of t
 his model in terms of Gibbs measures on permutations of\nthe integers. Thi
 s model can then be analyzed by means of geometric tools (based on\na quan
 tity called the flux of a permutation) in combination with probability est
 imates\nand cut-block arguments.\n\nOur result provides a full classificat
 ion of possible states of the system: For every temperature there are infi
 nitely many possible states\, all of them are translation invariant\, and 
 exactly one of them is concentrated on permutations consisting of finite c
 ycles only.\n  \nThe talk is based on joint work with Marek Biskup (UCLA).
 \n\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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