 93152 Andras Suto
 Percolation transition in the Bose gas
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May 26, 93

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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 BoseEinstein condensation is
accompanied by a percolation transition: the appearance of infinite cycles with
nonvanishing probability.
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