Fluctuation properties of the imperfect Bose gas

Abstract

The fluctuations of the occupation numbers of the different levels of the imperfect Bose gas are computed. They are neither normal, Gaussian, nor independent of the way the infinite volume limit is taken. The fluctuations of the overall density are on the contrary normal, Gaussian, and shape independent.

The canonical perfect Bose gas in Casimir boxes

“…(a) Since the paper by Buffet and Pulé [5] it has been known that there are differences in the fluctuations of the PBG condensate in the canonical and grand-canonical ensembles. We have shown that the picture becomes even more complicated if one passes to the case of Casimir boxes where there is already generalized BEC in the GCE.…”

“…But first we give some results which will be useful in all three cases. The basic identity for the canonical expectations at density ρ = n/V of the occupation numbers is (see [5] equation (10)):…”

“…Note that by Theorem 3.3 and comparison with the GCE, in this case there can only be condensation in states corresponding to n = (n 1 , 1, 1). The main tool in the technique developed in [5] and [6] is the following identity:…”

“…For example, it was shown in [5] that for the isotropic dilation of the canonical PBG the distribution of ground-state occupation number is different from the one in the GCE. The same is true for the fluctuations of the occupation numbers, which are shape dependent and are not normal or Gaussian.…”

A possible mechanism of concurring diagonal and off-diagonal long-range order for soft interactions

“…The ground state energy density reads e g.s. = t − |b|dρs q (33) where s q = lim S(q j )/V (for any j).…”