2001/12/31 by F. Cruz, Frederico F. de Souza Cruz, Marcus B. Pinto +4 · 4 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.1103/physreva.65.053613
published as Phys.Rev. A65 (2002) 053613 · 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002)
arxiv created 2002/03/21 · openalex publication_date 2002/05/09 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We use the nonperturbative linear \ensuremathδ expansion method to evaluate analytically the coefficients c1 and c2^\ensuremath'' that appear in the expansion for the transition temperature for a dilute, homogeneous, three-dimensional Bose gas given by Tc=T0(1+c1an1/3+[c2^\ensuremath'ln(an1/3)+c2^\ensuremath'']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 \ensuremathδ2 with the result c1=3.06. Here, we push the calculation to the next two orders obtaining c1=2.45 at order \ensuremathδ3 and c1=1.48 at order \ensuremathδ4. 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 c2^\ensuremath''=101.4, c2^\ensuremath''=98.2, and c2^\ensuremath''=82.9. Our analytical results seem to support the recent Monte Carlo estimates c1=1.32\ifmmode±\else\textpm\fi0.02 and c2^\ensuremath''=75.7\ifmmode±\else\textpm\fi0.4.