Bogoliubov-Tolmachev-Shirkov模型临界温度和能隙解的数值方法

数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1699-1711.

Bogoliubov-Tolmachev-Shirkov模型临界温度和能隙解的数值方法

葛志昊*(),李瑞华

河南大学数学与统计学院河南开封 475004

收稿日期:2018-12-19 出版日期:2020-12-26 发布日期:2020-12-29
通讯作者: 葛志昊 E-mail:zhihaoge@henu.edu.cn
基金资助:
国家自然科学基金(11971150);河南大学一流学科培育项目(2019YLZDJL08)

Numerical Methods for the Critical Temperature and Gap Solution of Bogoliubov-Tolmachev-Shirkov Model

Zhihao Ge*(),Ruihua Li

School of Mathematics and Statistics, Henan University, Henan Kaifeng 475004

Received:2018-12-19 Online:2020-12-26 Published:2020-12-29
Contact: Zhihao Ge E-mail:zhihaoge@henu.edu.cn
Supported by:
the NSFC(11971150);the Cultivation Project of First Class Subject of Henan University(2019YLZDJL08)

摘要/Abstract

摘要：

该文给出了近似求解超导理论中Bogoliubov-Tolmachev-Shirkov模型的临界温度和能隙解的最大-混合格式和最小-混合格式, 首次对具有变号核函数的上述模型给出了临界温度和能隙解的数值解, 给出了该数值方法的收敛性分析.最后给出了一些数值算例来验证理论结果.

关键词: Bogoliubov-Tolmachev-Shirkov模型, 临界温度, 能隙解, 收敛性分析

Abstract:

In the paper, the max-mixed scheme and min-mixed scheme are proposed for the critical temperature and gap solution of Bogoliubov-Tolmachev-Shirkov model in superconductivity theory. For the first time, the numerical solutions of critical temperature and gap solution are given for the above model with the alternating kernel function. The convergence analysis of the numerical method is also given. Also, some numerical examples are presented to verify the results of the paper.

Key words: Bogoliubov-Tolmachev-Shirkov model, Critical temperature, Gap solution, Convergence analysis

中图分类号:

O241.82

葛志昊,李瑞华. Bogoliubov-Tolmachev-Shirkov模型临界温度和能隙解的数值方法[J]. 数学物理学报, 2020, 40(6): 1699-1711.

Zhihao Ge,Ruihua Li. Numerical Methods for the Critical Temperature and Gap Solution of Bogoliubov-Tolmachev-Shirkov Model[J]. Acta mathematica scientia,Series A, 2020, 40(6): 1699-1711.

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参考文献 12

1	Bogoliubov N N , Tolmachev V V , Shirkov D V . A new method in the theory of superconductivity. Progress of Physics, 1958, 6 (11/12): 605- 682
2	Du Q , Yang Y . The critical temperature and gap solution in the Bardeen-Cooper-Schrieffer theory of superconductivity. Letters in Mathematical Physics, 1993, 29: 133- 150
3	Freiji A , Hainzl C , Seiringer R . The BCS gap equation for spin-polarized Fermions. Journal of Mathematical Physics, 2012, 53: 012101
4	Hainzl C , Seiringer R . Critical temperature and energy gap for the BCS equation. Physical Review B, 2008, 77: 184517
5	Hemmen L V . Linear fermion systems, molecular field models, and the KMS condition. Fortschr Phys, 1978, 26: 379- 439
6	Hugenholtz N M . Quantum theory of many-body systems. Rep Progr Phys, 1965, 28: 201- 247
7	Khalatnikov I M , Abrikosov A A . The modern theory of superconductivity. Adv Phys, 1959, 8: 45- 86
8	Rickayzen G. Theory of Superconductivity. New York: Interscience, 1965
9	Watanabe S . The solution to the BCS gap equation for superconductivity and its temperature dependence. Abstract and Applied Analysis, 2013, 2013: 932085
10	Yang Y . On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity. Letters in Mathematical Physics, 1991, 22: 27- 37
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