Andras Suto
Published 2002-04-19, updated 2007-03-20Version 4
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.
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
Journal: J. Phys. A: Math. Gen. 35 (2002) 6995-7002
The Mathematics of the Bose Gas and its Condensation
Dilute Hard "Sphere" Bose Gas in Dimensions 2, 4 and 5
Percolation transitions with nonlocal constraint
