Temperature dependence of the solution to the BCS gap equation for superconductivity

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540112
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Gunma University
• Principal Investigator: WATANABE Shuji 群馬大学, 大学院理工学府, 教授 (90222405)
• Co-Investigator(Kenkyū-buntansha): SAITOH Saburou 群馬大学, 名誉教授 (10110397)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 超伝導 / BCSギャップ方程式 / 温度依存性 / 不動点定理 / 非線形積分方程式

Outline of Final Research Achievements

The BCS theory is the successful quantum-mechanical theory of superconductivity. The basis of the BCS theory is the BCS gap equation.For temperatures small enough, we have shown that the solution to the BCS gap equation is continuous with respect to both the temperature and the wave vector on the basis of the Banach fixed-point theorem. For temperatures up to half of the transition temperature, we have shown that the solution is continuous with respect to both the temperature and the wave vector on the basis of the Schauder fixed-point theorem. Moreover, we have shown that the solution is Lipschitz continuous and monotonically decreasing with respect to the temperature.

Free Research Field

応用数学、応用解析学