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From the definition of a generalized conformable spatial derivative, an exponential conformable function with three parameters $(a,b,\alpha)$ is proposed for a viscous and an inertial-viscous steady-state Navier-Stokes 1D models, obtaining analytical solutions for both generalized conformable models. The conformable models' parameters are optimized to compare the viscous model to a Darcian 1D flow and the inertial-viscous model to a non-Darcian 1D model for a specific range of Darcy numbers $(1\times10^{-2}

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., Comment: 32 pages, 7 figures, 1 table

This article shows a new focus of mathematic analysis for the Solow-Swan economic growth model, using the generalized conformal derivative Katugampola (KGCD). For this, under the same Solow-Swan model assumptions, the Inada conditions are extended, which, for the new model shown here, depending on the order of the KGCD. This order plays an important role in the speed of convergence of the closed solutions obtained with this derivative for capital (k) and for per-capita production (y) in the cases without migration and with negative migration. Our approach to the model with the KGCD adds a new parameter to the Solow-Swan model, the order of the KGCD and not a new state variable. In addition, we propose several possible economic interpretations for that parameter., Comment: This paper was submitted in Physica A: Statistical Mechanics and its Applications on December 13, 2017

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 L\"uttinger model, our approach successfully overcomes the medium-intensity regime for quasi-particle 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., Comment: 19 pages, 9 figures. Physica Scripta (2018)

It is shown that in one-particle Schr\"{o}dinger quantum mechanics a small perturbation of a one-dimensional potential can produce a large change in the ground state, the effect becoming more pronounced with growing typical length of the potential, contrary to what standard stationary perturbation theory could make one believe.The possible consequences of this result for solid state physics and other fields are also discussed, and examples of such non-standard perturbations are furnished., Comment: 16 pages, 2 figures

The evolution of transverse-momentum-dependent effective band offset ($V_{\mathrm{eff}}$) profile for heavy (\emph{hh})- and light-holes (\emph{lh}), is detailed studied. Several new features in the metamorphosis of the standardized fixed-height $V_{\mathrm{eff}}$ profile for holes, in the presence of gradually increasing valence-band mixing and pseudomorphic strain, are presented. In some $III-V$ unstrained semiconducting layered heterostructures a fixed-height potential, is not longer valid for \emph{lh}. Indeed, we found ---as predicted for electrons---, permutations of the $V_{\mathrm{eff}}$ character for \emph{lh}, that resemble a "\emph{keyboard}", together with bandgap changes, whenever the valence-band mixing varies from low to large intensity. Strain is able to diminish the \emph{keyboard} effect on $V_{\mathrm{eff}}$, and also makes it emerge or vanish occasionally. We found that multiband-mixing effects and stress induced events, are competitors mechanisms that can not be universally neglected by assuming a fixed-height rectangular spatial distribution for fixed-character potential energy, as a reliable test-run input for heterostructures. Prior to the present report, neither direct transport-domain measurements, nor theoretical calculations addressed to these $V_{\mathrm{eff}}$ evolutions and permutations, has been reported for holes, as far as we know. Our results may be of relevance for promising heterostructure's design guided by valence-band structure modeling to enhance the hole mobility in $III-V$ materials., Comment: 15 pages, 6 figures. arXiv admin note: text overlap with arXiv:1302.6985

Shallow one-dimensional double well potentials appear in atomic and molecular physics and other fields. Unlike the "deep" wells of macroscopic quantum coherent systems, shallow double wells need not present low-lying two-level systems. We argue that this feature, the absence of a low-lying two-level system in certain shallow double wells, may allow the finding of new test grounds for quantum mechanics in mesoscopic systems. We illustrate the above ideas with a family of shallow double wells obtained from Bargman potentials through the Darboux-B\"{a}cklund transform., Comment: 9 pages, 2 figures

A model is presented, consisting of a single structureless particle on the line subject to a potential with three minima, with an exactly soluble ground level. In this model the ground level probability density becomes more sensitive to the global shape of the potential as the distance between the minima increases, so that for big enough distances small variations in the potential bring a qualitative change in the probability density, taking it from a unimodal, localized, distribution, to a bimodal one. We conjecture that this effect, of which we have not found any precedent in the literature, may be relevant in the design and characterization of mesoscopic devices such as triple quantum well systems., Comment: 20 pages, 8 figures

We present the metamorphosis in the effective-potential profile of layered heterostructures, for several III-V semiconductor binary compounds, when the band mixing of light and heavy holes increases. A root-locus-like procedure, is directly applied to an eigenvalue quadratic problem obtained from a multichannel system of coupled modes, in the context of multiband effective mass approximation. By letting grow valence-band mixing, it is shown the standard fixed-height rectangular potential-energy for the scatterer distribution, to be a reliable test-run input for heavy holes. On the contrary, this scheme is no longer valid for light holes and a mutable effective \emph{band offset} profile has to be considered instead, whenever the in-plane kinetic energy changes., Comment: 12 pages, 5 figures

The present article deals with Macroscopic Quantum Coherence resorting only to basic quantum mechanics. A square double well is used to illustrate the Leggett-Caldeira oscillations. The effect of thermal-radiation on two-level systems is discussed to some extent. The concept of decoherence is introduced at an elementary level. Handles are deduced for the energy, temperature and time scales involved in Macroscopic Quantum Coherence., Comment: 30 pages, 12 figures, 1 table