Transition temperature for weakly interacting homogeneous Bose gases

Abstract

We apply the nonperturbative optimized linear ␦ expansion method to the O(N) scalar field model in three dimensions to determine the transition temperature of a dilute homogeneous Bose gas. Our results show that the shift of the transition temperature ⌬T c /T c of the interacting model, compared with the ideal-gas transition temperature, really behaves as ␥an 1/3 where a is the s-wave scattering length and n is the number density. For Nϭ2 our calculations yield the value ␥ϭ3.059.

Bose-Einstein transition in a dilute interacting gas

“…[27] finite-size-scaling is used to reconcile this approach with the grand-canonical calculations. Reference [28] calculates T c with the help of an "optimized linear delta expansion, which avoids infrared divergencies and operates for any N ; for N = 2 the authors find c ∼ 3.0, but the validity of the method is difficult to assess, and the accuracy of this result may be affected by uncontrolled errors.…”

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].…”

“…Consequently, [19]. Another popular scheme is to use G 0 (p) = 1/p 2 [11,17,18,20,23]. This generates an unnatural one-loop contribution to ∆T c even in the absence of interactions.…”

“…Earlier attempts using resummed PT to determine ∆T c [11,17,18,19] have employed the linear δ expansion (LDE). These were criticized in Refs.…”

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

“…In a previous work the same method has been used to evaluate c1 to order-δ 2 with the result c1 = 3.06. Here, we push the calculation to the next two orders obtaining c1 = 2.45 at order-δ 3 and c1 = 1.48 at order-δ 4 . Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations.…”