  We present a theoretical study of transport properties through
superconducting contacts based on a new formulation of boundary conditions that
mimics interfaces for the quasiclassical theory of superconductivity. 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
reproduce results obtained by conventional quasiclassical boundary conditions,
or by boundary conditions based on the scattering approach. This 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. This approach is illustrated with the
calculation of Josephson currents through a variety of superconducting
junctions ranging from conventional to d-wave superconductors, and to the
analysis of supercurrent through a ferromagnetic nanoparticle. The calculation
of the current-voltage characteristics and of noise is applied to the case of a
contact between two d-wave superconductors. In particular, we discuss the use
of shot noise for the measurement of charge transferred in a multiple Andreev
reflection in d-wave superconductors.
