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Chinese Physics C

Critical temperature and condensed fraction of Bose-Einstein condensation in an external potential

Zhan-Jun Zhang, Qingshan Ma, Jun Zhang

Published Aug 1, 2011• 0 citations
Publisher

Abstract

Based on Bose-Einstein condensation at minimized momentum state, we get the expressions for the critical temperature and condensed fraction of Bose-Einstein condensation (BEC) in an external potential in the three-dimensional (3D) case. For the 1D and 2D cases, we present not only the critical temperature and corresponding particles but also the condition of BEC occurrence.

DOI
10.1088/1674-1137/35/8/005

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Based on Bose-Einstein condensation at minimized momentum state, we get the expressions for the critical temperature and condensed fraction of Bose-Einstein condensation (BEC) in an external potential in the three-dimensional (3D) case. For the 1D and 2D cases, we present not only the critical temperature and corresponding particles but also the condition of BEC occurrence.
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.
We present a scheme of analytical calculations determining the critical temperature and the number of condensed atoms of ideal gas Bose-Einstein condensation in external potentials with 1D, 2D or 3D periodicity. In particular we show that the width of the lowest energy band appears as the main parameter determining the critical temperature of condensation. Is obtained a very simple, proportional to 1/3 degree, regularity for this dependence. The fundamental role of tunneling in physics of condensate establishment is underscored.
The relationship of the critical temperature versus the total number of particles in different dimensional spaces,as well as the effect of the first-excited-state energy of particles on the critical temperature of low-dimensional Bose-Einstein condensation,are discussed in this paper.It is shown that the critical temperature in low-dimensional space increases more quickly than that in high-dimensional space with density of particle number increasing,and the critical temperature of system has close relation to the first-excited-state energy.In addition,even under the condition of absent special external potential,such as harmonic potential and power-law potential,the Bose-Einstein condensation can be realized at several K0 for excitons gas trapped in GaAs quantum well.