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

Abstract

We use the nonperturbative linear δexpansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 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 c_1 to order-δ^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-δ^3 and c_1=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. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.

29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002)

References in corpus (3)

• Transition temperature of a dilute homogeneous imperfect Bose gas
• Monte Carlo simulation of O(2) phi^4 field theory in three dimensions
• Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length

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