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The scattering problem in non-equilibrium quasiclassical theory of metals and superconductors: general boundary conditions and applications

I derive a general set of boundary conditions for quasiclassical transport theory of metals and superconductors that is valid for equilibrium and non-equilibrium situations and includes multi-band systems, weakly and strongly spin-polarized systems, and disordered systems. The formulation is in terms of the normal state scattering matrix. Various special cases for boundary conditions are known in the literature, that are however limited to either equilibrium situations or single band systems. The present formulation unifies and extends all these results. In this paper I will present the general theory in terms of coherence functions and distribution functions and demonstrate its use by applying it to the problem of spin-active interfaces in superconducting devices and the case of superconductor/half-metal interface scattering.