A bandmixing treatment for multiband-coupled systems via nonlinear-eigenvalue scenario

Nieva-Pérez, E.; Mendoza-Álvarez, E. A.; Diago‐Cisneros, L.; Duque, C.A.; Flores-Godoy, J.J.; Fernández‐Anaya, Guillermo

doi:10.1088/1402-4896/aaf752

Cited by 2 publications

(3 citation statements)

References 49 publications

(135 reference statements)

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“…where the vectors Γ j are certain (N × 1) spinors. Being independent of the spatial coordinates, the q j are the 2N eigenvalues which correspond to them as solution of the quadratic eigenvalue problem (QEP) [9,23] associated to (I.1). If we now substitute (IV.47) in (I.1) we have…”

Section: B Completely Orthonormalized Basismentioning

confidence: 99%

“…so that, for instance represents a typical QEP [21][22][23]. If P is Hermitian (formal Hermiticity), there is no a coupling term for first derivative states of the field F (z).…”

Section: B Completely Orthonormalized Basismentioning

confidence: 99%

“…All these filters have been used in former reports, indeed: (i) they were numerically evaluated for consistency [16]; (ii) they have been quoted to work out expected values for quantum transport entities within the MMST [9], and more recently, some of them were successfully invoked in related problems [10,23]. As punchline, we next illustrate in Fig.…”

Section: Symmetry Relationsmentioning

confidence: 99%

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Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries

Diago-Cisneros,

Flores-Godoy,

Fernández-Anaya

2020

Preprint

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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 × N ) interacting components (for N ≥ 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. Contents I. Introductory outline II. Flux Tunneling III. Structured unitarity of S A. EFA general case: N ≥ 2 B. EFA particular case: N = 4 C. Reduction from the structured case to the generalized one. IV. Convergence from EFA to EMA: flux and unitarity A. Limit of uncoupled N -component flux 1. Flux Convergence 2. Reduction of the structured-unitarity: N ≥ 2 3. Reduction of the generalized-unitarity: N = 4 B. Completely Orthonormalized Basis V. Symmetry Relations VI. Tunneling amplitudes A. Probabilities Flux Conservation 1.

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Section: B Completely Orthonormalized Basismentioning

confidence: 99%

“…so that, for instance represents a typical QEP [21][22][23]. If P is Hermitian (formal Hermiticity), there is no a coupling term for first derivative states of the field F (z).…”

Section: B Completely Orthonormalized Basismentioning

confidence: 99%