General form of the Green’s function regular at infinity for the homogeneous Sturm–Liouville matrix operator

Pernas-Salomón, René; Pérez‐Álvarez, R.; Velasco, V.R.

doi:10.1016/j.amc.2015.08.001

Cited by 2 publications

(4 citation statements)

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“…being B(z), W(z) and Y(z) = −P † (z), (N × N) general-hermitian matrices [27,29]. Hereinafter, O N stands for the null N-order matrix.…”

Section: Quadratic Eigenvalue Problem 221 Generalized Matrix Sturm-li...mentioning

confidence: 99%

“…Whenever these theoretical models are invoked within the EFA for real MMS-layered heterostructures, more restrictions arise due the presence of topological requirements at the boundaries and at the interfaces. This type of problem is well-known as N-coupled components GSL matrix boundaryequation [27][28][29], which for MMS heterostructures with translational symmetry in the [x, y] plane of perfect interfaces, can be cast as follows…”

Section: Extended Kohn Lüttinger (Kl) Hamiltonianmentioning

confidence: 99%

“…There are two targets focused in the present study. Firstly, to obtain the eigen-spinors of the QEP that underlies an Ncoupled components generalized Sturm-Liouville (GSL) matrix boundary-equation [27][28][29]. By modeling coupled MMS, we recall the generalized Schur decomposition (GSD), the simultaneous triangularization (STR) and root-locus-like techniques to describe the dynamics of heavy holes (hh), light holes (lh) and spin-split holes (sh) in layered semiconductor heterostructures.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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We present a numeric-computational procedure to deal with the intricate bandmixing phenomenology in the framework of the quadratic eigenvalue problem (QEP), which is derived from a physical system described by N-coupled components Sturm-Liouville matrix boundary-equation. The modeling retrieves the generalized Schur decomposition and the root-locus-like techniques to describe the dynamics of heavy holes (hh), light holes (lh) and spin-split holes (sh) in layered semiconductor heterostructures. By exercising the extended (N = 6) Kohn Lüttinger model, our approach successfully overcomes the medium-intensity regime for quasiparticle coupling of previous theoretical studies. As a bonus, the sufficient conditions for a generalized QEP have been refined. The sh-related off -diagonal elements in the QEP mass-matrix, becomes a competitor of the bandmixing parameter, leading the hh-sh and lh-sh spectral distribution to change, then they can not be disregarded or zeroed, as was assumed in previous theoretical studies. Thereby, we unambiguously predict that several of the new features detected for hh-lh-sh spectral properties and propagating modes, become directly influenced by the metamorphosis of the effective band-offset scattering profile due sub-bandmixing effects strongly modulated with the assistance of sh, even at low-intensity mixing regime.

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“…being B(z), W(z) and Y(z) = −P † (z), (N × N) general-hermitian matrices [27,29]. Hereinafter, O N stands for the null N-order matrix.…”

Section: Quadratic Eigenvalue Problem 221 Generalized Matrix Sturm-li...mentioning

confidence: 99%

Section: Extended Kohn Lüttinger (Kl) Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…For example, transfer matrix variants to avoid the numerical instability known as Omega-d problem, have been reported recently [17]. For the study of matched systems, a general and compact form for the Greens function regular at infinity for the homogeneous Sturm-Liouville matrix operator was also reported [18].…”

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confidence: 99%

Ubiquity of the Sturm-Liouville problem in multilayer systems

Álvarez

Pernas-Salomón

2016

EPL

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We postulate a general Lagrangian density which leads to the equations of motion of the well-known cases of the electromagnetic field, the theory of elasticity, and some other particular problems in classical physics. When the mentioned cases are studied in multilayer systems, i.e., when the constitutive parameters depend on one of the Cartesian coordinates, all of them lead us to a matrix Sturm-Liouville problem whose equation of motion, in its most general form, can be derived from the postulated Lagrangian density too. These results demonstrate the ubiquitous character of the Sturm-Liouville matrix problem and consequently the relevance of its study from the mathematical, physical and numerical point of view. The consequences of this curious result are briefly analyzed.

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General form of the Green’s function regular at infinity for the homogeneous Sturm–Liouville matrix operator

Cited by 2 publications

References 20 publications

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

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

Ubiquity of the Sturm-Liouville problem in multilayer systems

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