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CATEGORIES:Probability
SUMMARY:The free Bose gas and permutations of integers - T
homas Richthammer (Munich)
DTSTART;TZID=Europe/London:20130115T163000
DTEND;TZID=Europe/London:20130115T173000
UID:TALK40510AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40510
DESCRIPTION:Using Feynman's representation\, the equilibrium s
tate of the Bose gas can be described in terms of
a probabilistic model\, similar to models from non
-quantum statistical mechanics. In this model a pa
rticle configuration is characterized by the posit
ions of the particles in combination with a permut
ation of the particles. The natural mathematical\n
framework for such a particle model is an infinite
volume description\, but in the case of\nthe Bose
gas model this infinite volume description is sti
ll missing: The main difficulty here is to incorpo
rate the particle permutations into the model.\n\n
In order to show how to overcome this difficulty w
e consider a toy model\, where the particle positi
ons are fixed at the vertices of the integer latti
ce. We introduce an infinite volume description of
this model in terms of Gibbs measures on permutat
ions of\nthe integers. This model can then be anal
yzed by means of geometric tools (based on\na quan
tity called the flux of a permutation) in combinat
ion with probability estimates\nand cut-block argu
ments.\n\nOur result provides a full classificatio
n of possible states of the system: For every temp
erature there are infinitely many possible states\
, all of them are translation invariant\, and exac
tly one of them is concentrated on permutations co
nsisting of finite cycles only.\n \nThe talk is b
ased on joint work with Marek Biskup (UCLA).\n\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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