Unitarity and symmetries of the multicomponent scattering matrix

Abstract

We present a theoretical procedure, which is fundamental for unitarity preservation in multicomponent–multiband systems, for a synchronous mixed-particle quantum transport. This study focuses the problem of (N×N) interacting components (with N≥2), in the framework of the envelope function approximation (EFA), and the standard unitary properties of the (N=1) scattering matrix are recovered. Rather arbitrary conditions to the basis-set and/or to the output scattering coefficients, are not longer required to preserve flux conservation, if the eigen-functions are orthonormalized in both the configuration and the spinorial spaces. We predict that the present approach, is valid for different kind of multiband–multicomponent physical systems of coupled charge–spin carriers, within the EFA, with small transformations if any. We foretell the interplay for the state-vector transfer matrix eigen-values, together with the large rates of its condition number, as novel complementary tools for a more accurate definition of the threshold for tunneling channels in a scattering experiment.