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

Qiang Du, Yisong Yang

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)133-150
Number of pages18
JournalLetters in Mathematical Physics
Volume29
Issue number2
DOIs
StatePublished - Oct 1 1993

Keywords

  • Mathematics Subject Classifications (1991): 82B26, 83D55, 45G10, 45L

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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