- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 932085, 5 pages
The Solution to the BCS Gap Equation for Superconductivity and Its Temperature Dependence
Division of Mathematical Sciences, Graduate School of Engineering, Gunma University, 4-2 Aramaki-machi, Maebashi 371-8510, Japan
Received 27 May 2013; Accepted 9 August 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 Shuji Watanabe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Physical Review, vol. 108, pp. 1175–1204, 1957.
- N. N. Bogoliubov, “A new method in the theory of superconductivity. I,” Soviet Physics, vol. 34, pp. 41–46, 1958.
- F. Odeh, “An existence theorem for the BCS integral equation,” Journal of Research and Development, vol. 8, pp. 187–188, 1964.
- P. Billard and G. Fano, “An existence proof for the gap equation in the superconductivity theory,” Communications in Mathematical Physics, vol. 10, pp. 274–279, 1968.
- A. Vansevenant, “The gap equation in superconductivity theory,” Physica D, vol. 17, no. 3, pp. 339–344, 1985.
- R. L. Frank, C. Hainzl, S. Naboko, and R. Seiringer, “The critical temperature for the BCS equation at weak coupling,” The Journal of Geometric Analysis, vol. 17, no. 4, pp. 559–567, 2007.
- C. Hainzl, E. Hamza, R. Seiringer, and J. P. Solovej, “The BCS functional for general pair interactions,” Communications in Mathematical Physics, vol. 281, no. 2, pp. 349–367, 2008.
- C. Hainzl and R. Seiringer, “Critical temperature and energy gap for the BCS equation,” Physical Review B, vol. 77, Article ID 184517, 2008.
- J. M. Ziman, Principles of the Theory of Solids, Cambridge University Press, London, UK, 1972.
- S. Watanabe, “A mathematical proof that the transition to a superconducting state is a second-order phase transition,” Far East Journal of Mathematical Sciences, vol. 34, no. 1, pp. 37–57, 2009.
- S. Watanabe, “The solution to the BCS gap equation and the second-order phase transition in superconductivity,” Journal of Mathematical Analysis and Applications, vol. 383, no. 2, pp. 353–364, 2011.
- S. Watanabe, “Addendum to ‘The solution to the BCS gap equation and the second-order phase transition in superconductivity’,” Journal of Mathematical Analysis and Applications, vol. 405, no. 2, pp. 742–745, 2013.