An Application of Third Formalism of Quantum Statistics and a Diagonalization Theorem in Asymptotic Exact Theory of Superconductivity

Abstract

Starting from an electron-phonon interacting model, by means of the third formalism of quantum statistics, and with the aid of a diagonalization theorem, the Tc of superconductors from weak coupling to strong coupling cases are studied in a unified way. Our results are comparable with those of McMillan's theory, (which is valid up to the electron-phonon (e-ph) coupling parameter λ~1, a good agreement is shown for λ<1.3) and the Allen and Dynes's theory. Especially our results are very close to those of Hg spectrum with λ~2.0 and some strong coupling compounds. The theory is exact in the thermodynamic limit, without introducing variation method, the compensation of the dangerous diagrams in finite order in perturbation theory, abnormal green's function etc.