 05146 Teunis C. Dorlas, Philippe A. Martin and Joseph V. Pule
 Long Cycles in a Perturbed Mean Field Model of a Boson Gas
(330K, Postscript)
Apr 25, 05

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. In this paper we give a precise mathematical formulation of the relation
between Bose condensation and long cycles and prove its validity for the perturbed mean field model
of a Bose gas.
We decompose the total density $\rho=\rho_{{\rm short}}+\rho_{{\rm long}}$
into the number density of particles belonging to cycles of finite length ($\rho_{{\rm short}}$)
and to infinitely long cycles ($\rho_{{\rm long}}$) in the thermodynamic limit. For this model we
prove that when there is Bose condensation, $\rho_{{\rm long}}$ is different from zero and identical
to the condensate density. This is achieved through an application of the theory of
large deviations. We discuss the possible equivalence of
$\rho_{{\rm long}}\neq 0$ with offdiagonal long range order and winding paths
that occur in the path integral representation of the Bose gas.
 Files:
05146.src(
05146.keywords ,
Cycles.pdf.mm )