Rigorous proof of isotope effect by Bardeen-Cooper-Schrieffer theory

Research output: Contribution to journalArticle

Abstract

In this article, we present a rigorous proof of the isotope effect within the theory of Bardeen-Cooper-Schrieffer for isotropic superconductors. We show that, when the interaction kernel is a positive constant, the isotope effect is exact; when the interaction kernel is a positive function depending on the energies of the pairing electrons, the isotope effect is no longer exact but lies within a sharp range determined by the varying kernel function. Moreover, we show that our method here may be extended to establish an existence and uniqueness theorem for the transition temperature in the Bogoliubov-Tolmachev-Shirkov model which allows separate phonon and Coulomb dominance in their respective energy regimes.

Original languageEnglish (US)
Pages (from-to)2009-2025
Number of pages17
JournalJournal of Mathematical Physics
Volume44
Issue number5
DOIs
StatePublished - May 1 2003

Fingerprint

BCS theory
isotope effect
existence theorems
kernel
uniqueness theorem
kernel functions
Existence and Uniqueness Theorem
Superconductor
Phonon
Kernel Function
Energy
Interaction
Pairing
transition temperature
interactions
Electron
energy
Range of data
electrons
Model

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Rigorous proof of isotope effect by Bardeen-Cooper-Schrieffer theory. / Yang, Yisong.

In: Journal of Mathematical Physics, Vol. 44, No. 5, 01.05.2003, p. 2009-2025.

Research output: Contribution to journalArticle

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