- 01-87 Daniel Ueltschi
- Geometric and probabilistic aspects of boson lattice models
(143K, LaTeX2e with 8 postscript figures)
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 Lennard-Jones potential is studied as an example
of a system where first-order phase transitions occur.
A major interest of bosonic systems is the possibility of displaying a
Bose-Einstein condensation. This is discussed in the light of the main
existing rigorous result, namely its occurrence in the hard-core boson
model. Finally, we consider another approach that involves the lengths
of the cycles formed by the particles in the space-time representation;
Bose-Einstein condensation should be related to positive probability of
infinite cycles.
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01-87.src(
01-87.comments ,
01-87.keywords ,
probo.tex ,
figcont.eps ,
figcyc1.eps ,
figcyc2.eps ,
figfeykac.eps ,
figgse.eps ,
figphd.eps ,
figpot.eps ,
figsptime.eps )