Grand Canonical Versus Canonical Ensemble: Universal Structure of Statistics and Thermodynamics in a Critical Region of Bose-Einstein Condensation of an Ideal Gas in Arbitrary Trap

作者：Tarasov S V; Kocharovsky Vl V; Kocharovsky V V

来源：Journal of Statistical Physics, 2015, 161(4): 942-964.

DOI：10.1007/s10955-015-1361-3

• Bose-Einstein condensation
• Critical phenomena
• Critical region
• Grand canonical ensemble
• Canonical ensemble
• Mesoscopic system

We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics and thermodynamics in the critical region of Bose-Einstein condensation. It is valid for an arbitrary trap, loaded with an ideal gas, in the thermodynamic limit. We show that for the quantities, changing by a finite amount across the critical region, the exact GCE result differs from the corresponding canonical-ensemble result by a factor on the order of unity even in the thermodynamic limit. Thus, a widely used GCE approach does not describe correctly the critical phenomena at the phase transition for the actual systems with a fixed number of particles and yields only an asymptotics far outside the critical region.

• 出版日期2015-11