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

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 off-diagonal long range order and winding paths 
that occur in the path integral representation of the Bose gas.