Percolation transition in the Bose gas II
Statistical Mechanics
2009-11-07 v4 Mathematical Physics
math.MP
Abstract
In an earlier paper (J. Phys. A: Math. Gen. 26 (1993) 4689) we introduced the notion of cycle percolation in the Bose gas and conjectured that it occurs if and only if there is Bose-Einstein condensation. Here we give a complete proof of this statement for the perfect and the imperfect (mean-field) Bose gas and also show that in the condensate there is an infinite number of macroscopic cycles.
Keywords
Cite
@article{arxiv.cond-mat/0204430,
title = {Percolation transition in the Bose gas II},
author = {Andras Suto},
journal= {arXiv preprint arXiv:cond-mat/0204430},
year = {2009}
}
Comments
The paper is completed with the proof of Eq. (34) and with a remark after Eq. (44) on the existence for any m>ln(rho/rho_0) of an infinite cycle which contains a fraction between exp{-(m+1)} and exp{-m} of the total number of particles