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arXiv:hep-th/0010213 · Modern Physics Letters B

D-DIMENSIONAL IDEAL QUANTUM GASES IN A Arn+Br-n POTENTIAL

Ahmed Jellal, Mohammed Daoud A

Published Oct 30, 2003• 7 citations
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Abstract

This paper is concerned with thermostatistics of both D-dimensional Bose and Fermi ideal gases in a confining potential of type Arn+Br-n, where A, B are strictly positive constants and n is the power-law exponent. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like the density of states, density profiles and the number of particles. Bose–Einstein condensation (BEC) is discussed in the high and low temperature limits corresponding to T→∞ and T→0, respectively.

DOI
10.1142/s021798490300630x

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This paper is concerned with thermostatistics of both D-dimensional Bose and Fermi ideal gases in a confining potential of type Arn+Br-n, where A, B are strictly positive constants and n is the power-law exponent. The investigation is performed in the framework of the semiclassical approximation. Some physical quantities for such systems are derived, like the density of states, density profiles and the number of particles. Bose–Einstein condensation (BEC) is discussed in the high and low temperature limits corresponding to T→∞ and T→0, respectively.
We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. From such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose–Einstein condensation can set up in a confining power-law potential if and only if D/2+D/n>1, where D is the space dimension and n is the power-law exponent.
Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in ddd dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.
The thermostatistical properties of an ideal gas of q -deformed bosons trapped in a D -dimensional power-law potential are studied, based on the q -deformed Bose–Einstein distribution. The effects of q -deformation on the properties of the system are discussed. It is shown that q -deformed bosons ( q ≠ 1) possess many different characteristics from those of ordinary bosons, which include the condition that Bose–Einstein condensation (BEC) occurs, the critical temperature and the continuity of heat capacity.
The critical temperature for Bose-Einstein condensation, ground-state fraction, and heat capacity of an ideal gas of Bose particles that are confined by an n-dimensional generic power-law potential trap are derived. The conditions for Bose-Einstein condensation and the discontinuous conditions of the heat capacity at critical temperature are obtained. All these quantities and conditions are found to vary markedly with the dimensionality of space, characteristics of particles, and shape of the external potential. The results obtained here are universal.