The model is based on the characteristics of BEC at finite temperature from the view of free energy variance of the canonical system.The expression of the shift of the critical temperature in BEC is derived and given and theoretical argument is provided for similar experiments in BEC in the paper.
Based on grand canonical assembles statistics,the Bose Einstein Condensation (BEC) in non interacting bound atomic system is studied.Some basic concepts of BEC in conventional infinite Bose system are extended.The condition of chemical potential μ ≤0 will not be guarantted for the present finite bound system,and the vapour with μ 0,the state without condensation at any eigenstate,might be possible in principle even below a critical temperature T C .Gibbs functions for both the gas and the BEC state at temperature TT C have been calculated.The condition for BEC to appear is presented.The relation of BEC temperature T C with the density of particles is estimated and the result is qualitatively in good agreement with the experimental results.
Abstract This chapter describes the mechanism of Bose–Einstein condensation in the simplest ideal Bose gas case. An explicit expression for the critical temperature is derived in the analytically soluble case of a gas confined in a box. Various thermodynamic quantities are calculated above and below the critical temperature. Emphasis is given to the isothermal compressibility which diverges below the critical temperature. The behaviour of the off-diagonal one-body density matrix is discussed. Results for the fluctuations of the single-particle occupation numbers are derived in both the canonical and grand canonical ensembles.
We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that Bose-Einstein(B-E) statistics needs a correction for finite system at ultralow temperatures. As a corrected statistics we introduced a Tsallis type of generalized B-E statistics. The condensate fraction calculated with this generalized B-E statistics, is satisfied well with the experimental result. In the third section we show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached. Our results support the experimental result which was obtained well below the condensation temperature. In the fourth section we concentrate on the thermodynamic Casimir force on the Bose-Einstein condensate. We explored the temperature dependence of the Casimir force.