Eilenberger equations for moderately dirty superconductors

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Abstract
Weak dependence of the Eilenberger Green’s functions f(v→) upon the direction v→ at the Fermi surface is explored to obtain equations for the averages 〈f(v→)〉=F over the Fermi surface. The derivation is similar to that of Usadel for the dirty limit. The proposed equations, however, are valid not only in the extreme dirty limit, but for ‘‘moderately dirty’’ samples too, i.e., in the case most often encountered in experiment. The formalism also describes superconductivity in a weak field for any impurity concentration and at any temperature.