PERCOLATION TRANSITION IN THE BOSE-GAS

The canonical partition function of a Bose gas gives rise to a probabi lity distribution over the permutations of N particles. We study the p robability and mean value of the cycle lengths in the cyclic permutati ons, their relation to physical quantities like pair correlations, and their thermodynamic limit. We show that in the ground state of most i nteracting boson gases the mean cycle length diverges in the bulk limi t 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 non-vanishing probability.