Andras Suto 
Percolation transition in the Bose gas
(61K, LateX)

ABSTRACT.  The canonical partition function of a Bose gas gives rise to a probability 
distribution over the permutations of $N$ particles. We study the probability
and mean value of the cycle lengths in the cyclic permutations, their relation
to physical quantities like pair correlations, and their thermodynamic limit.
We show that in the ground state of most interacting 
boson gas the mean cycle length diverges in the bulk limit and the particles
form macroscopic cycles. In the free Bose gas Bose-Einstein condensation is
accompanied by a percolation transition: the appearance of infinite cycles with
nonvanishing probability.