Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

الأصل · EN

We use the nonperturbative linear δexpansion method to evaluate analytically the coefficients c₁ and c₂′ ′ which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by Tc= T₀ {1 + c₁ a n¹/³ + [c₂′ (a n¹/³) +c₂′ ′] a² n²/³ + O (a³ n)}, where T₀ is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c₁ to order-δ² with the result c₁= 3.06. Here, we push the calculation to the next two orders obtaining c₁=2.45 at order-δ³ and c₁=1.48 at order-δ⁴. 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. At the same orders we obtain c₂′′=101.4, c₂′ ′=98.2 and c₂′ ′=82.9. Our analytical results seem to support the recent Monte Carlo estimates c₁=1.32 ± 0.02 and c₂′ ′= 75.7 ± 0.4.