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Superconducting Phase in the BCS Model with Imaginary Magnetic Field
http://hdl.handle.net/2261/0002005208
http://hdl.handle.net/2261/0002005208aba5deee-c346-4818-b46e-a45551caa78b
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms280101.pdf (1006.5 KB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
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| 公開日 | 2022-06-23 | |||||||
| タイトル | ||||||||
| タイトル | Superconducting Phase in the BCS Model with Imaginary Magnetic Field | |||||||
| 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 | tree expansion | |||||||
| 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
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| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | We prove that in the reduced quartic BCS model with an imaginary external magnetic field a spontaneous $U(1)$-symmetry breaking (SSB) and an off-diagonal long range order (ODLRO) occur. The system is defined on a hyper-cubic lattice with periodic boundary conditions at positive temperature. In the free part of the Hamiltonian we assume the nearest-neighbor hopping. The chemical potential is fixed so that the free Fermi surface does not degenerate. The term representing the interaction between electrons' spin and the imaginary external magnetic field is the $z$-component of the spin operator multiplied by a pure imaginary parameter. The SSB and the ODLRO are shown in the infinite-volume limit of the thermal average over the full Fermionic Fock space. The magnitude of the negative coupling constant must be larger than a certain value so that the gap equation is solvable. The gap equation is different from that of the conventional mean field BCS model because of the presence of the imaginary magnetic field. By adjusting the imaginary magnetic field this model shows the SSB and the ODLRO in high temperature, weak coupling regimes where the conventional reduced BCS model does not show these phenomena. The proof is based on Grassmann Gaussian integral formulations and a double-scale integration scheme to analytically control the formulations. | |||||||
| 言語 | en | |||||||
| 書誌情報 |
en : Journal of Mathematical Sciences The University of Tokyo 巻 28, 号 1, p. 1-179, 発行日 2021-06-18 |
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| 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 | ||||||||
| 2017-03-21 | ||||||||
