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Journal of Shanxi Normal University

Bose-Einstein Condensation and the Factors of Affecting the Particle Density-of-state

Xin Jun-li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

At first,this paper has discussed that the state density of particle relates to dimension n of particle space motion and different energy in ideal condition(there is not external potential field).On this basis,We also draw a conclusion that the particle density-of-state not only relates to the dimension of space motion but also the property of the external potential field.

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Physical Review A•Nov 1, 1999•17 citations
At first,this paper has discussed that the state density of particle relates to dimension n of particle space motion and different energy in ideal condition(there is not external potential field).On this basis,We also draw a conclusion that the particle density-of-state not only relates to the dimension of space motion but also the property of the external potential field.
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.
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.
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.