Quasiclassical description of transport through superconducting contacts

We present a formulation of boundary conditions that mimics interfaces for the quasiclassical theory of superconductivity and that are suitable for the analysis of transport properties of a great variety of superconducting contacts. These boundary conditions are based on a description of an interface in terms of a simple Hamiltonian. We show how this Hamiltonian description is incorporated into quasiclassical theory via a T-matrix equation by integrating out irrelevant energy scales right at the onset. The resulting boundary conditions are then explicitly shown to reproduce results obtained by conventional quasiclassical boundary conditions, or by boundary conditions based on the scattering approach. The presented formalism is well suited for the analysis of magnetically active interfaces as well as for calculating time-dependent properties such as the current-voltage characteristics or as current fluctuations in junctions with arbitrary transmission and bias voltage. As a particular implementation of the boundary conditions, we discuss the use of shot noise for the measurement of charge transferred in a multiple Andreev reflection in d-wave superconductors.