Tc for homogeneous dilute Bose gases: a second-order result

الأصل · EN

The transition temperature for a dilute, homogeneous, three-dimensional Bose gas has the expansion Tc = T₀ 1 + c₁ a n(1/3) + [c₂' ln(a n(1/3)) + c₂''] a² n(2/3) + O(a³ n), where a is the scattering length, n the number density, and T₀ the ideal gas result. The first-order coefficient c₁ depends on non-perturbative physics. In this paper, we show that the coefficient c₂' can be computed perturbatively. We also show that the remaining second-order coefficient c₂'' depends on non-perturbative physics but can be related, by a perturbative calculation, to quantities that have previously been measured using lattice simulations of three-dimensional O(2) scalar field theory. Making use of those simulation results, we find Tc = T₀ 1 + (1.32+-0.02) a n(1/3) + [19.7518 ln(a n(1/3)) + (75.7+-0.4)] a² n(2/3) + O(a³ n).