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High Energy Physics - Theory
Title: Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model
(Submitted on 27 Dec 2023 (v1), last revised 9 Apr 2024 (this version, v2))
Abstract: We study the convergence of the Ginzburg-Landau (GL) expansion in the context of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the Nambu-Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature $T$ and chemical potential $\mu$. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap $\Delta$ and dynamical quark mass $M$ are given by $\Delta_\text{conv} = \pi T$ and $M_\text{conv} = \sqrt{\mu^2 + (\pi T)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.
Submission history
From: William Gyory [view email][v1] Wed, 27 Dec 2023 01:19:52 GMT (236kb,D)
[v2] Tue, 9 Apr 2024 21:34:08 GMT (242kb,D)
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