Bose-Einstein condensation of ideal Bose gases under external conditions

G.S. Rosa

Wenji Deng

Klaus Kirsten

This chapter focuses on the applications involving finite temperature theories. Technically, the grand canonical partition function is easiest to handle and in general it is the one used for the analysis of the thermodynamical properties. In fact, for properties like the energy and the specific heat of the gas this is justified because in the thermodynamical limit the different ensembles are known to give the same answer. The chapter uses the grand canonical ensemble to obtain properties like critical temperature, energy and specific heat. It summarizes the grand canonical description of ideal Bose gases trapped by magnetic fields and describes the formulation of Bose-Einstein condensation as a symmetry-breaking phenomenon.

Klaus Kirsten, David J. Toms

Lawrence J. Landau, Ivan F. Wilde

Wu Bo

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.