| Project/Area Number |
21540110
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Gunma University |
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Principal Investigator |
WATANABE Shuji 群馬大学, 大学院・工学研究科, 教授 (90222405)
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| Co-Investigator(Kenkyū-buntansha) |
SAITOH Saburou 群馬大学, 名誉教授 (10110397)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 不動点定理 / 陰関数定理 / BCSギャップ方程式 / 超伝導 / 温度 / 2次相転移 / 熱力学的ポテンシャル / 熱力学ポテンシャル / Schauderの不動点定理 |
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| Research Abstract |
We study the solution to the BCS gap equation in the BCS model of superconductivity. When the potential is a positive constant, we establish the existence and uniqueness of the solution so as to show smoothness of the solution on the basis of the implicit function theorem. When the potential is not a constant, we next show how the solution varies with the temperature on the basis of the Schauder fix-point theorem. Approximating the solution by a function of class C2 , we then show that the phase transition to a superconducting state is a second-order phase transition.
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