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Journal of Yunyang Teachers College

The Two-dimensional Ideal Bose Gas

Qiao An-qin

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The thermodynamic characteristics of the two-dimensional idea Bose gas have been studied by using approximate analytic calculations. The result shows that there is no Bose-Einstein condensation without external trap. The capacity entropy and pressure are studied under strong degeneroy and weak degeneroy. In the case of weak degeneroy, the thermodynamic characteristics of the two dimensional ideal Bose gas tend to be that of classical condition.

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The thermodynamic characteristics of the two-dimensional idea Bose gas have been studied by using approximate analytic calculations. The result shows that there is no Bose-Einstein condensation without external trap. The capacity entropy and pressure are studied under strong degeneroy and weak degeneroy. In the case of weak degeneroy, the thermodynamic characteristics of the two dimensional ideal Bose gas tend to be that of classical condition.
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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.
We study thermodynamic properties of a one-dimensional ideal Bose gas trapped by a steep potential of an exponential type U(q)=U0[e(2q/a)b−1]. Fugacity, energy, and heat capacity of such a system are calculated for various combinations of the potential parameters as well for several values of the number of particles N. Both the thermodynamic limit and finite N are considered. Estimations for the single-particle spectrum asymptotics are obtained in the analytical form involving the Lambert W function. In the thermodynamic limit, the Bose–Einstein condensation is predicted for 0 < b < 2. We associate such behavior with an effective temperature-dependent space dimensionality arising due to the influence of the external potential of the analyzed type.