 0187 Daniel Ueltschi
 Geometric and probabilistic aspects of boson lattice models
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Mar 2, 01

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Abstract. This review describes quantum systems of bosonic particles moving
on a lattice. These models are relevant in statistical physics, and
have natural ties with probability theory. The general setting is
recalled and the main questions about phase transitions are addressed.
A lattice model with LennardJones potential is studied as an example
of a system where firstorder phase transitions occur.
A major interest of bosonic systems is the possibility of displaying a
BoseEinstein condensation. This is discussed in the light of the main
existing rigorous result, namely its occurrence in the hardcore boson
model. Finally, we consider another approach that involves the lengths
of the cycles formed by the particles in the spacetime representation;
BoseEinstein condensation should be related to positive probability of
infinite cycles.
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0187.src(
0187.comments ,
0187.keywords ,
probo.tex ,
figcont.eps ,
figcyc1.eps ,
figcyc2.eps ,
figfeykac.eps ,
figgse.eps ,
figphd.eps ,
figpot.eps ,
figsptime.eps )