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  1. 121 数理科学研究科
  2. Journal of Mathematical Sciences, the University of Tokyo
  3. 28
  4. 3
  1. 0 資料タイプ別
  2. 30 紀要・部局刊行物
  3. Journal of Mathematical Sciences, the University of Tokyo
  4. 28
  5. 3

Superconducting Phase in the BCS Model with Imaginary Magnetic Field. III. Non-Vanishing Free Dispersion Relations

http://hdl.handle.net/2261/0002005796
http://hdl.handle.net/2261/0002005796
f980cb2b-a24a-479a-9772-e547f01ee21d
名前 / ファイル ライセンス アクション
jms280301.pdf jms280301.pdf (1.1 MB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2022-10-25
タイトル
タイトル Superconducting Phase in the BCS Model with Imaginary Magnetic Field. III. Non-Vanishing Free Dispersion Relations
言語 en
言語
言語 eng
キーワード
言語 en
主題Scheme Other
主題 The BCS model
キーワード
言語 en
主題Scheme Other
主題 spontaneous symmetry breaking
キーワード
言語 en
主題Scheme Other
主題 off-diagonal long range order
キーワード
言語 en
主題Scheme Other
主題 Grassmann integral formulation
キーワード
言語 en
主題Scheme Other
主題 multi-scale IR analysis
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
著者 Kashima, Yohei

× Kashima, Yohei

en Kashima, Yohei

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抄録
内容記述タイプ Abstract
内容記述 We analyze a class of the BCS model, whose free dispersion relation is non-vanishing, under the influence of imaginary magnetic field at positive temperature. The magnitude of the negative coupling constant must be small but is allowed to be independent of the temperature and the imaginary magnetic field. The infinite-volume limit of the free energy density is characterized. A spontaneous symmetry breaking and an off-diagonal long range order are proved to occur only in high temperatures. This is because the gap equation in this model has a positive solution only if the temperature is higher than a critical value. The proof is based on a double-scale integration of the Grassmann integral formulation. In this scheme we integrate with the infrared covariance first and with the ultra-violet covariance afterwards, which is opposite to the previous schemes in [Kashima, Y., J. Math.\ Sci.\ Univ.\ Tokyo {\bf 28} (2021), 1--179], [Kashima, Y., J. Math.\ Sci.\ Univ.\ Tokyo {\bf 28} (2021), 181--398] or \cite{K_BCS_I}, \cite{K_BCS_II} in short. As the other focus, we study geometric properties of the phase boundaries, which are periodic copies of a closed curve in the two-dimensional space of the temperature and the real time variable. Here we adopt the real time variable in place of the temperature times the imaginary magnetic field by considering its relevance within contemporary physics of dynamical phase transition at positive temperature. As the main result, we show that for any choice of a non-vanishing free dispersion relation the representative curve of the phase boundaries has only one local minimum point, or in other words the phase boundaries do not oscillate with temperature, if and only if the minimum of the magnitude of the free dispersion relation over the maximum is larger than the critical value $\sqrt{17-12\sqrt{2}}$. Overall we use the same notational conventions as in \cite{K_BCS_I}, \cite{K_BCS_II}. So this work is a continuation of these preceding papers.
言語 en
書誌情報 en : Journal of Mathematical Sciences The University of Tokyo

巻 28, 号 3, p. 399-556, 発行日 2021-08-30
ISSN
収録物識別子タイプ ISSN
収録物識別子 13405705
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AA11021653
Mathmatical Subject Classification
en
82D55(MSC2010)
Mathmatical Subject Classification
en
81T28(MSC2010)
出版者
出版者 Graduate School of Mathematical Sciences, The University of Tokyo
言語 en
原稿受領日
2019-03-25
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