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業績詳細


【論文】

The solution to the BCS gap equation and the second-order phase transition in superconductivity
【全著者名】
Shuji Watanabe
【掲載雑誌名】
Journal of Mathematical Analysis and Applications
【巻・号・頁】
383(2): 353-364
【発表年月】
2011年11月
【単著、共著の別】
単著
【掲載雑誌種別】
学術雑誌
【論文の種別】
原著
【要旨】
The existence and the uniqueness of the solution to the BCS gap equation of superconductivity is established in previous papers, but the temperature dependence of the solution is not discussed. In this paper, in order to show how the solution varies with the temperature, we first give another proof of the existence and the uniqueness of the solution and point out that the unique solution belongs to a certain set. Here this set depends on the temperature $T$. We define another certain subset of a Banach space consisting of continuous functions of both $T$ and $x$. Here, $x$ stands for the kinetic energy of an electron minus the chemical potential. Let the solution be approximated by an element of the subset of the Banach space above. We second show, under this approximation, that the transition to a superconducting state is a second-order phase transition.
【キーワード】
BCS gap equation, second-order phase transition, superconductivity, nonlinear integral equation, Schauder fixed-point theorem
【外部リンク】
http://www.elsevier.com/locate/jmaa/
【DOI】
doi:10.1016/j.jmaa.2011.05.025

【研究者】

渡辺 秀司
【筆頭著者】
筆頭著者