On the Bose-Einstein condensation of an ideal gas

Fabrice P. Laussy

Guy B. Standen, David J. Toms

Andrei I. Pavlov, V. S. Babichenko, Ilya Polishchuk

Sun Chang-yong, Wang Jisuo

The general expressions of energy, heat capacity and Bose - Einstein condensation (BEC) temperature are given for an n-dimensional ideal Bose gas with a dispersion relation of , with which the possibility of occurrence of BEC can be determined. The curve of against temperature of the gas with is continuous at , while that of the gas with has a finite jump . These are two different kinds of phase transitions.

S.R. DE GROOT, Cornelis A. Ten Seldam

Luca Salasnich

In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1