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Journal of Zhangzhou Normal University

Bose-Einstein Condensation of an Ideal Bose Gas Trapped in the Low Dimensional Space

Liu Jing-yi

Published Jan 1, 2001• 0 citations
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Abstract

By using the local density approximation, Bose-Einstein condensation of Bose gas in the low dimensional space is investigated. The results show that when a proper external potential is taken, BEC may occur in the low dimensional space. The critical temperature Tc, the ground state fraction N0/N and the behaviour (jump or not) of the heat capacity C depend on the shape of the potential.

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By using the local density approximation, Bose-Einstein condensation of Bose gas in the low dimensional space is investigated. The results show that when a proper external potential is taken, BEC may occur in the low dimensional space. The critical temperature Tc, the ground state fraction N0/N and the behaviour (jump or not) of the heat capacity C depend on the shape of the potential.
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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 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.
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