Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries

• URL: http://arxiv.org/abs/2010.15926v2
• Date: Fri, 9 Jul 2021 21:06:01 GMT
• Title: Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries
• Authors: L. Diago-Cisneros, J. J. Flores-Godoy and G. Fern\'andez-Anaya
• Abstract summary: We derive a robust theoretical procedure, which is fundamental in quantum-transport problems for unitarity preservation. We predict 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multicomponent-multiband fluxes of spim-charge carriers, whose components propagate mixed and synchronously, with \emph{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 \emph{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 \emph{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.

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