Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries

Multicomponent-multiband fluxes of spim-charge carriers, whose components propagate mixed and synchronously, with a priori nonzero incoming amplitudes, do not obey the standard unitarity condition on the scattering matrix for an arbitrary basis set. For such cases, we have derived a robust theoretical procedure, which is fundamental in quantum-transport problems for unitarity preservation and we have named after structured unitarity condition. Our approach deals with \(N times N\) interacting components for $N geq 2$, within the envelope function approximation (EFA), and yet 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, if the eigen-functions are orthonormalized in both the configuration and the spinorial spaces. We expect the present model to be workable, for different kind of multiband-multicomponent physical systems described by Hermitian Hamiltonians within the EFA, with small transformations if any. We foretell the interplay for the state-vector transfer matrix, together with the large values of its condition number, as a novel complementary tools for a more accurate definition of the threshold for tunnelling channels in a scattering experiment.