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Journal of Physics A Mathematical and Theoretical

Thermodynamic properties of a trapped relativistic Bose gas with pair production

Guozhen Su, Liwei Chen, Jincan Chen

Published Jun 19, 2008• 8 citations
Publisher

Abstract

An ideal gas of relativistic bosons trapped in a D -dimensional power-law potential is explored, where the possibility of particle–antiparticle pair production is taken into account. Expressions for several important parameters, such as the critical temperature of Bose–Einstein condensation (BEC), ground-state fraction and heat capacity, are analytically derived and used to discuss the relevant properties of the system. An important parameter χ is introduced to mark the extent of the relativistic effects on the characteristics of BEC. It is found that the correction of the critical temperature due to the relativistic effects is considerable for the system with a large parameter χ. It is more important to show that the pair production may lead to several novel characteristics for a relativistic Bose gas, such as the high temperature BEC, the rapid increase of the heat capacity at high temperatures and the disappearance of the anomaly of the heat capacity at the critical temperature in the ultrarelativistic limit.

DOI
10.1088/1751-8113/41/28/285002

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An ideal gas of relativistic bosons trapped in a D -dimensional power-law potential is explored, where the possibility of particle–antiparticle pair production is taken into account. Expressions for several important parameters, such as the critical temperature of Bose–Einstein condensation (BEC), ground-state fraction and heat capacity, are analytically derived and used to discuss the relevant properties of the system. An important parameter χ is introduced to mark the extent of the relativistic effects on the characteristics of BEC. It is found that the correction of the critical temperature due to the relativistic effects is considerable for the system with a large parameter χ. It is more important to show that the pair production may lead to several novel characteristics for a relativistic Bose gas, such as the high temperature BEC, the rapid increase of the heat capacity at high temperatures and the disappearance of the anomaly of the heat capacity at the critical temperature in the ultrarelativistic limit.
Statistical properties of an ideal gas of relativistic fermions trapped in a D-dimensional power-law potential are studied, in which the effect of particle–antiparticle pair production is taken into account. It is shown that the relativistic effect is considerable even at very low temperatures for the system with Fermi energy comparable with the rest energy of a particle. In contrast, the effect of pair production is significant at high temperatures, but negligible at low temperatures. Moreover, it is found that the pair production results in several novel characteristics, such as the asymptotic behavior of chemical potential and rapid increase of heat capacity in the high temperature region.
Bose–Einstein condensation of an ideal relativistic Bose gas trapped in a generic power-law potential is investigated. The analytical expressions for some important parameters such as the critical temperature, ground-state fraction and heat capacity are derived. The general criteria on the occurrence of Bose–Einstein condensation and the discontinuity of heat capacity at the critical temperature are obtained. The results obtained here present a unified description for the Bose–Einstein condensation of a class of ideal Bose systems so that many important conclusions in the literature are included in this paper.
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.
The q -deformed Bose–Einstein distribution derived from the q -boson algebra is used to study the low-temperature behavior of an ideal q -deformed Bose gas with relativistic energy spectrum. The effects of q -deformation on the properties relative to Bose–Einstein condensation (BEC) are discussed. It is shown that q -deformation leads to some novel characteristics different from those of an original Bose gas, which include the criteria on the occurrence of BEC, critical temperature and jump of heat capacity at the critical point. The results obtained here provide a unified description for the properties of q -deformed Bose systems from the nonrelativistic case to the ultrarelativistic limit, so that some important conclusions in the literature are included in this paper.
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 properties of a trapped ideal Bose gas in n -dimensional space are studied. General analytic expressions of the critical temperature of Bose-Einstein condensation, the jump of heat capacity at and the fraction of condensation at temperatures below have been derived. How these physical quantities depend on the external potential, particle characteristics and space dimensionality are discussed. We find that when a proper external potential is taken, Bose-Einstein condensation may occur in any dimensional space.