Canonical statistics of trapped ideal and interacting Bose gases

Abstract

The mean ground state occupation number and condensate fluctuations of interacting and non-interacting Bose gases confined in a harmonic trap are considered by using a canonical ensemble approach. To obtain the mean ground state occupation number and the condensate fluctuations, an analytical description for the probability distribution function of the condensate is provided directly starting from the analysis of the partition function of the system. For the ideal Bose gas, the probability distribution function is found to be a Gaussian one for the case of the harmonic trap. For the interacting Bose gas, using a unified approach the condensate fluctuations are calculated based on the lowest-order perturbation method and on Bogoliubov theory. It is found that the condensate fluctuations based on the lowest-order perturbation theory follow the law δ 2 N0 ∼ N , while the fluctuations based on Bogoliubov theory behave as N 4/3 .

Number-of-particle fluctuations and stability of Bose-Einstein-condensed systems

“…But the contradictory results in Refs. [3,7,8,11] with that in Refs. [9,12] within the same Bogoliubov approximation deserve further investigation.…”

“…Particularly, even for the Bogoliubov approximation, both γ = 4/3 [3,5,7,8,11] and γ = 1 [9,12] scaling laws have been obtained.…”

“…Recently the number-of-particle fluctuation of interacting Bose-condensed systems has attracted much theoretical attention, but whether or not it is anomalous still has not been resolved, since different methods predict different values of γ [3,4,5,6,7,8,9,10,11,12]. Particularly, even for the Bogoliubov approximation, both γ = 4/3 [3,5,7,8,11] and γ = 1 [9,12] scaling laws have been obtained.…”

“…In Refs. [3,7,8,11], the spectrum obtained by the Bogoliubov approximation was used and a γ = 4/3 scaling law was obtained for the non-condensate number-of-particle fluctuation. However using the compressibility sum rule (see Eq.…”

Condensate fluctuations of interacting Bose gases within a microcanonical ensemble

“…Statistical properties [5][6][7][8][9][10] and, in particular, condensate fluctuations have been investigated for ideal and weakly interacting Bose gases (WIBGs), both within the canonical [11][12][13][14][15][16][17][18][19][20][21] and microcanonical [11,18,19,[21][22][23][24] ensembles, where the differences between ideal…”