Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

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dc.creatorKneur, Jean-Loic
dc.creatorPinto, Marcus B.
dc.creatorRamos, Rudnei O.
dc.date2002-07-11
dc.date2003-08-06
dc.date.accessioned2026-07-07T02:46:13Z
dc.date.available2026-07-07T02:46:13Z
dc.descriptionWe investigate the convergence properties of optimized perturbation theory, or linear $δ$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.
dc.description38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev. A
dc.identifierhttps://arxiv.org/abs/cond-mat/0207295
dc.identifierhttp://arxiv.org/abs/cond-mat/0207295
dc.identifierPhys.Rev. A68 (2003) 043615
dc.identifierdoi:10.1103/PhysRevA.68.043615
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/19587
dc.subjectSoft Condensed Matter
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectHigh Energy Physics - Theory
dc.titleAsymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem
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