arXiv:cond-mat/0405537

Effects of constraints on the phase transition to Bose-Einstein condensation

Velin G. Ivanov

Published May 23, 2004• 1 citation

Abstract

Classic and recent results for the critical behaviour of ideal Bose gas at constant volume and constant pressure and for various spatial dimensionalities d>0 are reviewed. New results about the critical properties in a close vicinity of the $λ-$point are presented.

DOI: 10.48550/arxiv.cond-mat/0405537

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arXiv:cond-mat/0405537

Effects of constraints on the phase transition to Bose-Einstein condensation

Velin G. Ivanov

Published May 23, 2004• 1 citation

arXiv HTML PDF

Abstract

λ-

point are presented.

DOI: 10.48550/arxiv.cond-mat/0405537

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P. Lacour-Gayet, G. Toulouse

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Bose–Einstein condensation in mesoscopic systems: The self-similar structure of the critical region and the nonequivalence of the canonical and grand canonical ensembles

Vl. V. Kocharovsky, Vl. V. Kocharovsky, Sergey V. Tarasov

The analytical theory of Bose–Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose–Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose–Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose–Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose–Einstein condensation has been given.The analytical theory of Bose–Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose–Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose–Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose–Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose–Einstein condensation has been given.

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Ralf Beckmann, F. Karsch, David E. Miller

Physical Review AJan 1, 198238 citations

λ-

point are presented.

{V}_{c}=O(\frac{N}{\mathrm{ln}N})

, which is both necessary and sufficient for the onset of Bose-Einstein condensation in the system. For instance, if the system is now cooled even at constant volume

V(={V}_{c})

, the condensate fraction gradually builds up and becomes nonnegligible as

T

approaches ${T}_{0}\ensuremath{\simeq}\frac{({T}_{c})}{2}$; below

{T}_{0}

, it grows steadily as $(1\ensuremath{-}\frac{T}{{T}_{0}})$. On the other hand, if we continued to cool the system at constant

P

its volume, over a thermodynamically negligible range of temperatures, would reduce to values

O({N}^{\frac{1}{2}})

which, in turn, would be accompanied by an abrupt accumulation of practically all the particles of the system into the single-particle ground state ${\ensuremath{\epsilon}}_{0}$. The specific heat

{C}_{P}

, after having passed through a maximum, would also finally reduce to subextensive values. Phase transitions of this kind may be of relevance to the physical behavior of thin helium films and helium submonolayers.