arXiv:quant-ph/0410065 · AIP conference proceedings

On phase transitions in Bose gases at constant density and constant pressure

Velin G. Ivanov

Published Jan 1, 2004• 0 citations

Abstract

The phase transitions in Bose gases at constant volume and constant pressure are considered. New results for the chemical potential, the effective Landau‐Ginzburg free energy and the equation of state of the Bose‐Einstein condensate in ideal Bose gases with a general form of the energy spectrum are presented. Unresolved problems are discussed.

DOI: 10.1063/1.1828417

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arXiv:quant-ph/0410065 · AIP conference proceedings

On phase transitions in Bose gases at constant density and constant pressure

Velin G. Ivanov

Published Jan 1, 2004• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.1063/1.1828417

Related papers

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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.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.

arXiv:cond-mat/0405537May 23, 20041 citation

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Yu. M. Poluéktov

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L. Goldstein

The peculiar condensation in phase space of ideal Bose-Einstein gases is discussed when the internal energy states of the atoms or molecules is taken into account and when the gas of atoms without internal structure is placed in an external conservative field of force. The inclusion of the internal energy states decreases while the application of the external field increases the condensation temperature from its value in absence of either of these causes. The transition phenomenon, apart from the preceding change in the condensation temperature, proceeds in the same way as in the case of the free gas atoms without internal structure; in particular, the order of the transition remains invariable, as the continuity of the heat capacity at constant volume is maintained at the transition point.The peculiar condensation in phase space of ideal Bose-Einstein gases is discussed when the internal energy states of the atoms or molecules is taken into account and when the gas of atoms without internal structure is placed in an external conservative field of force. The inclusion of the internal energy states decreases while the application of the external field increases the condensation temperature from its value in absence of either of these causes. The transition phenomenon, apart from the preceding change in the condensation temperature, proceeds in the same way as in the case of the free gas atoms without internal structure; in particular, the order of the transition remains invariable, as the continuity of the heat capacity at constant volume is maintained at the transition point.

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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.