Critical Temperature of Bose-Einstein Condensation of Hard-Sphere Gases

Abstract

We determine the critical temperature of a 3-d homogeneous system of hard-sphere Bosons by path-integral Monte Carlo simulations and finite-size scaling. At low densities, we find that the critical temperature is increased by the repulsive interactions, in the form of a power law in density with exponent 1/3: ∆TC /T0 ∼ (na 3 ) 1/3 . At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.

Bose-Einstein transition in a dilute interacting gas

“…This provides a possible explanation for the discrepancy of the different Monte Carlo results [20,23,24] and [19]; whereas Refs. [20,23,24] calculated the linear corrections directly in the limit n 1/3 a → 0, Ref.…”

“…A surprise came when the Monte Carlo calculations for hard sphere bosons were extended to lower densities and showed, in addition to the depression of T c at high densities, the existence of a low density regime where the critical temperature is indeed increased by the interaction [19]. At very low densities the shift of the critical temperature was found to be ∆T c T 0 field theoretical problem in three spatial dimensions.…”

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas in variational perturbation theory through six loops

“…One of the basic questions is about the nature and size of the shift of the BEC transition temperature due to the interactions. Although attempts at the problem have a long history [1,2], only the recent advent of experimental realizations of BEC in dilute gases have prompted considerable work to finally solve the problem both qualitatively and quantitatively [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Here we treat the case of a homogenous gas as opposed to, e.g., the case of a harmonic trap [21].…”

“…[13,14] for explanations of the low MC value in Ref. [4]; see Ref. [13] for a critique of the MC calculation of Ref.…”

Superfluid transition temperature from the Lindemann-like criterion

“…By now it is generally believed that if the density increases T λ first rise with respect to the ideal gas value, but the exact form of the correction to Eq. (1) still remains, to some extent, a point of controversy, despite the large number of recent investigations [4][5][6][7][8][9][10][11][12] .…”