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

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

2001-12-17

arxiv.org/abs/cond-mat/0112306v2

Phys.Rev. A65 (2002) 053613

Physics

Condensed Matter

Soft Condensed Matter

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

Scientific paper

10.1103/PhysRevA.65.053613

We use the nonperturbative linear \delta expansion 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-\delta^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-\delta^3 and c_1=1.48 at order-\delta^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.

Affiliated with

Also associated with

No associations

Rating

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-261402