Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909164649840640 |
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| author | Gyory, William Yamamoto, Naoki |
| author_facet | Gyory, William Yamamoto, Naoki |
| contents | 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 $μ$. 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 $Δ$ and dynamical quark mass $M$ are given by $Δ_\text{conv} = πT$ and $M_\text{conv} = \sqrt{μ^2 + (πT)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16372 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model Gyory, William Yamamoto, Naoki High Energy Physics - Theory Superconductivity High Energy Physics - Phenomenology Nuclear Theory 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 $μ$. 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 $Δ$ and dynamical quark mass $M$ are given by $Δ_\text{conv} = πT$ and $M_\text{conv} = \sqrt{μ^2 + (πT)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition. |
| title | Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model |
| topic | High Energy Physics - Theory Superconductivity High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2312.16372 |