By using the generalized Bose-Einstein distribution function,Bose-Einstein condensation of a generalized Bose gases trapped in a generic power-law potential in the two dimensional space is investigated.Analytical expressions such as critical temperature that Bose-Einstein condensation occurs,the ground state fraction and heat capacity are derived.The influence of the nonextensive parameter on the thermostatistic properties of a generalized Bose gases is discussed.

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Quantum Distribution Functions in Non-Equilibrium Statistical Mechanics

Robert F. O’Connell

NATO ASI series. Series B : PhysicsJan 1, 19862 citations

Physics Letters A

On the generalized distribution functions of quantum gases

Qiuping-A. Wang, Alain Le Méhauté

Published Nov 1, 1997• 32 citations

Publisher

DOI: 10.1016/s0375-9601(97)00621-x

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A

of the equilibrium distribution function in terms of the pressure and temperature gradients and time derivatives, though a closed expression for this coefficient as a function of

v

and

T

is known only in limiting cases; (b) The function

W

of the general equation of state for ideal gases in all statistics

pv=(\frac{\mathrm{RT}}{M})W({v}^{\frac{2}{3}}T)

is adiabatically invariant. Numerical values of the viscosity and heat conductivity coefficients, which should come out of the formal theory on the introduction of special assumptions about the molecular forces, have not yet been obtained. It is our hope that these results, when found, may furnish an experimental test of the existence of Einstein-Bose statistics in real gases, as is required by theory.

For an ideal statistical gas, where

PV=sE

, all thermodynamic functions can be derived from

G(V,T)

, i.e.,

A(V,T)

is given by a suitable integration over

G(V,T)

. Since $G={N}_{\ensuremath{\mu}}$, the normalization constant, $\ensuremath{\mu}(V,T)$, of the distribution function is sufficient to provide a complete thermodynamic description of such a system. With the aid of the $\ensuremath{\aleph}$-theorem it is shown that there is a sharp physical distinction between the degenerate and non-degenerate Bose-Einstein gases; to any given density there corresponds a transition temperature between them. The method developed is applied to the general (relativistic and non-relativistic) non-degenerate quantum and degenerate Fermi-Dirac gases.