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Letters in Mathematical Physics

, Volume 29, Issue 2, pp 133–150 | Cite as

The critical temperature and gap solution in the Bardeen-Cooper-Schrieffer theory of superconductivity

  • Qiang Du
  • Yisong Yang
Article

Abstract

The Letter studies the problem of numerical approximations of the critical transition temperature and the energy gap function in the Bardeen-Cooper-Schrieffer equation arising in superconductivity theory. The positive kernel function leads to a phonon-dominant state at zero temperature. Much attention is paid to the equation defined on a bounded region. Two discretized versions of the equation are introduced. The first version approximates the desired solution from below, while the second, from above. Numerical examples are presented to illustrate the efficiency of the method. Besides, the approximations of a full space solution and the associated critical temperature by solution sequences constructed on bounded domains are also investigated.

Mathematics Subject Classifications (1991)

82B26 83D55 45G10 45L 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Qiang Du
    • 1
  • Yisong Yang
    • 2
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsCarnegie Mellon UniversityPittsburghUSA

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