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Physical Review Letters

Bose-Einstein Condensation of a Relativistic Gas in d Dimensions

Ralf Beckmann, Frithjof Karsch, David E. Miller

Published Oct 29, 1979• 58 citations
Publisher

Abstract

This Letter investigates the conditions for Bose-Einstein condensation of an ideal relativistic Bose gas in different spatial dimensions. It is shown that the thermodynamical properties of the critical particle density are qualitatively different for massive and massless relativistic Bose particles.
DOI
10.1103/physrevlett.43.1277

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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.
We discuss the properties of an ideal relativistic Bose gas with nonzero chemical potential $\ensuremath{\mu}$ (i.e., with net charge) but differ from all previous discussions by including the effects of antiparticles. We obtain for the first time the relevant high-temperature expansion, emphasizing the constraint $|\ensuremath{\mu}|<~m$, and show that a box of massless particles can have a net charge even though $\ensuremath{\mu}=0$. Finally, we discuss the properties of Bose-Einstein condensation for both massless and massive bosons in ddd space dimensions.
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.
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.