Zu de Gennes’ Methode der Korrelationsfunktion in der Theorie der Supraleitung

Abstract

At a second order transition, gap function and transition temperature of a superconductor can be determined from a linear integral equation. According to DE GENNES, the kernel of this integral equation may be obtained from a correlation function. This relation between correlation function and kernel is critically discussed. It is shown that the quantum mechanical correlation function is to be replaced by its slowly varying part, and it is suggested that the latter may be calculated from classical mechanics. The classical correlation function can be expressed as a momentum integral over a distribution in phase space developing with time according to the laws of classical mechanics. In the presence of statistically distributed impurities, the distribution function obeys the BOLTZMANN equation. Finally, the mathematical formulation of reflection properties of surfaces is discussed.