Physical Review A - Atomic, Molecular, and Optical Physics
We use the nonperturbative linear δ expansion method to evaluate analytically the coefficients c1 and c''2 that appear in the expansion for the transition temperature for a dilute, homogeneous, three-dimensional Bose gas given by Tc=T0(1+c1an1/3+[c′2ln(an1/3)+c''2]a2n2/3+O(a3n)), 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. Analyzing 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=101.4, c''2=98.2, and c''2=82.9. Our analytical results seem to support the recent Monte Carlo estimates c1=1.32±0.02 and c''2=75.7±0.4.
de Souza Cruz, Frederico F. F.; Pinto, Marcus; Ramos, Rudnei O.; and Sena, Paulo, "Higher-Order Evaluation of the Critical Temperature For Interacting Homogeneous Dilute Bose Gases" (2002). Open Dartmouth: Faculty Open Access Articles. 1927.