Method of quasiclassical Green's functions in the theory of transport phenomena in superconducting mesoscopic structures

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A short introduction to the theory of matrix quasiclassical Green's functions is given and possible applications of this theory to transport properties of mesoscopic superconducting-normal metal (S/N) structures are considered. We discuss a simplified version of these equations in the diffusive regime and in the case of a weak proximity effect. These equations are used for the calculation of the conductance of different S/N structures. Long-range, phase-coherent effects are studied in a 4-terminal S/N/S structures under conditions when the Josephson critical current is negligible. It is shown that the Josephson effects may be observed in this system if an additional current flows through the N electrode.