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Journal of Chongqing University of Science and Technology

Producing Condition on Bose-Einstein Condensation of Any Dimensional Ideal Bose System

Wu Bo

Published Jan 1, 2012• 0 citations
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Abstract

According to generic relation between particle's energy and momentum,we adopt the common procedure of quanta statistics which firstly work out the grand partition function,the critical temperature and producing condition of any dimensional ideal Bose system.With no external potential and in the thermodynamics condition,it is shown that the producing condition of any dimensional ideal Bose-Einstein Condensation only lies on the size relation between space dimensionality of particle and momentum's index in energy expression,which is a universal conclusion.For it,we can explain no Bose-Einstein Condensation with no external potential and under low dimensional spaces.

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According to generic relation between particle's energy and momentum,we adopt the common procedure of quanta statistics which firstly work out the grand partition function,the critical temperature and producing condition of any dimensional ideal Bose system.With no external potential and in the thermodynamics condition,it is shown that the producing condition of any dimensional ideal Bose-Einstein Condensation only lies on the size relation between space dimensionality of particle and momentum's index in energy expression,which is a universal conclusion.For it,we can explain no Bose-Einstein Condensation with no external potential and under low dimensional spaces.
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 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 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 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.
The density of states and thermodynamic properties of an ideal gas system trapped in a generic power-law potential in an n -dimensional space are studied. A unified description for the Bose, Fermi and classical gases is given by using the grand potential of the system. Consequently, not only the results in current textbooks of statistical mechanics but also some new general important conclusions, such as the conditions for the occurence of Bose-Eisntein condensation in a trapped Bose system in any dimensional space, can be derived directly using the results of this paper.