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Long-period systems and superlattices, with additional periodicity, have new effects on the energy spectrum and wave functions. Most approaches adjust theories for infinite systems, which is acceptable for large but not small number of unit cells $n$. In the past 30 years, a theory based entirely on transfer matrices was developed, where the finiteness of $n$ is an essential condition. The theory of finite periodic systems (TFPS) is also valid for any number of propagating modes, and arbitrary potential profiles (or refractive indices). We review this theory, the transfer matrix definition, symmetry properties, group representations, and relations with the scattering amplitudes. We summarize the derivation of multichannel matrix polynomials (which reduce to Chebyshev polynomials in the one-propagating mode limit), the analytical formulas for resonant states, energy eigenvalues, eigenfunctions, parity symmetries, and discrete dispersion relations, for superlattices with different confinement characteristics. After showing the inconsistencies and limitations of hybrid approaches that combine the transfer-matrix method with Floquet's theorem, we review some applications of the TFPS to multichannel negative resistance, ballistic transistors, channel coupling, spintronics, superluminal, and optical antimatter effects. We review two high-resolution experiments using superlattices: tunneling time in photonic band-gap and optical response of blue-emitting diodes, and show extremely accurate theoretical predictions., 57 pages, 33 figures

Recently, an approach for metallic superlattices based on the finite periodic systems theory was introduced \cite{Pereyra2020}. Unlike most, if not all, of the published approaches that are valid in the $n \rightarrow \infty $ limit, the finite periodic approach is valid for any natural number $n$ and allows one to determine analytical expressions for scattering amplitudes and dispersion relations. It was shown, for frequencies below $\omega_{p}$ and large metallic-layer thickness, that under the common assumption that fields inside conductors move along the so-called "true" angle that defines the orientation of the constant-phase planes, anomalous results appear with an apparent parity effect. This issue is addressed here and it is shown that those results are due to the lack of unitarity and the underlying phenomena of absorption and loss of energy. Two compatible approaches are presented here to solve the lack of unitarity and to account for the absorption phenomenon. We show that by keeping the complex angles, the principle of flux conservation is fully satisfied, above and below $\omega_p$. This approach, free of assumptions, gives us light to improve the formalism when the real angle assumption is made. We show that by taking into account the induced currents and the requirement of flux conservation, we end up with an improved approach, with new Fresnel and transmission coefficients, fully compatible with those of the complex-angle approach., Comment: 16 pages and 12 figures

We study the time evolution of the survival probability and the spin polarization of a dissipative nondegenerate two-level system in the presence of a magnetic field in the Faraday configuration. We apply the Extended Gaussian Orthogonal Ensemble approach to model the stochastic system-environment interaction and calculate the survival and spin polarization to first and second order of the interaction picture. We present also the time evolution of the thermal average of these quantities as functions of the temperature, the magnetic field, and the energy-levels density, for ρ(ϵ)∝ϵs, in the subohmic, ohmic, and superohmic dissipation forms. We show that the behavior of the spin polarization calculated here agrees rather well with the time evolution of spin polarization observed and calculated, recently, for the electron-nucleus dynamics of Ga centers in dilute (Ga,N)As semiconductors.

The reason why the effective-mass approximation, derived for wave packets constructed from infinite-periodic-systems' wave functions, works so well with nanoscopic structures, has been an enigma and a challenge for theorists. To explain and clarify this issue, we re-derive the effective-mass approximation in the framework of the theory of finite periodic systems, i.e., using energy eigenvalues and fast-varying eigenfunctions, obtained with analytical methods where the finiteness of the number of primitive cells per layer, in the direction of growth, is a prerequisite and an essential condition. This derivation justifies and explains why the effective-mass approximation works so well for nano-structures. We show also with explicit optical-response calculations that the rapidly varying eigenfunctions $\Phi_{\epsilon_0,\eta_0}(z)$ of the one-band wave functions $\Psi^{\epsilon_0,\eta_0}_{\mu,\nu}(z)= \Psi^{\epsilon_0}_{\mu,\nu}(z) \Phi_{\epsilon_0,\eta_0}(z)$, can be safely dropped out for the calculation of inter-band transition matrix elements., Comment: 6 pages

Using the analytical expressions for the genuine eigenfunctions $\varphi_{\mu\nu}(z)$ and eigenvalues $E_{\mu,\nu}$, of open, bounded and quasi-bounded finite periodic systems, we derive the eigenfunctions space-inversion symmetry relations. The superlattice eigenfunctions symmetries, closely related with the symmetries and zeros of the Chebyshev polynomials of the second kind $U_n$, are fully written in terms of the number of unit cells $n$, the subband index $\mu$ and the intra-subband index $\nu$., Comment: 10 pages, 14 figures

We study the spin dynamics of a 2DEG moving across a magnetic superlattice. We describe the spin transitions induced by sectionally homogeneous tilted magnetic fields and the spatial evolution of spin-1/2 wave functions: amplitude and phase, in terms of the tilting angle, the Fermi energy and the magnetic field strengths. Clear signatures of coherent spin mixing and coherent spin flipping processes are shown. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the effects of charge polarization on the extended physical properties of superlattices, such as transmission coefficients and valence band structure. We consider both linear and parabolic modulation of the band edge. Based on the theory of finite periodic systems, analytic expressions and high precision calculations of the relevant physical quantities for n-cell systems are obtained. Well-known features of these systems are identified. Besides the well-known energy band structure, we have also the field band structure, with interesting characteristics. Wider field gaps at stronger internal electric fields and higher density of field bands for larger layer widths are some of these characteristics. Well defined level density asymmetries identify the minibands induced by charge polarization or the so-called quantum confining Stark effect. We present the n-cell transmission amplitudes, transmission coefficients and miniband structures for different values of the relevant parameters.

A phenomenological theory to describe the electromagnetic properties of granular superconductors, based on known bulk superconductors expressions and conventional Josephson's junctions tunneling currents, is presented and succesfully used to fit distinct experimental results for the magnetic susceptibility as a function of the temperature and the applied magnetic field of rather different samples., Comment: 6 pages, 6 figures

In the new approach to study the optical response of periodic structures, successfully applied to study the optical properties of blue-emitting InGaN/GaN superlattices, the spontaneous charge polarization was neglected. To search the effect of this quantum confined Stark phenomenon we study the optical response, assuming parabolic band edge modulations in the conduction and valence bands. We discuss the consequences on the eigenfunction symmetries and the ensuing optical transition selection rules. Using the new approach in the WKB approximation of the finite periodic systems theory, we determine the energy eigenvalues, their corresponding eigenfunctions and the subband structures in the conduction and valence bands. We calculate the photoluminescence as a function of the charge localization strength, and compare with the experimental result. We show that for subbands close to the barrier edge the optical response and the surface states are sensitive to charge polarization strength., Comment: 6 figures

An important drawback of the standard theory, describing light-emitting periodic structures, is the lack of explicit knowledge of the initial and final states. In the new approach, based on the theory of finite periodic systems, the superlattice eigenvalues and eigenfunctions, are rigorously and explicitly determined. This approach provides the possibility of a truly quantum calculation of the optical response of periodic structures. New selection rules, tunable surface-energy-levels repulsion and interesting optical-spectra effects, related to intra-subband and surface states, are reported. Most of the actually observed transitions, “forbidden” for the standard approach, become allowed. The unexplained phenomenon of clustering of narrow peaks, observed in high-resolution blue-laser spectra by Nakamura et al. , are now fully explained and faithfully reproduced. The higher accuracy of this approach and the feasibility to control the detachment of the surface energy levels are important improvements relevant to optical-physics and the technological and biomedical applications.

A different approach to calculate the I−V characteristics of p+(Ga,Mn)As/n+GaAs spin injectors is presented. The vanishing of the spin-extraction transmission coefficients at the spin-split valence-band edges leads us to predict a dip or plateau in the I−V characteristics of this kind of diodes. We show that this minimum, or the inflection point, shifts with the exchange energy. Within this approach and using Kane-like densities of states with a detached impurity band, and exchange energies reported in the literature, excellent agreement is found with observed low-bias features of I−V characteristics.

This book presents a comprehensive course of quantum mechanics for undergraduate and graduate students. After a brief outline of the innovative ideas that lead up to the quantum theory, the book reviews properties of the Schrödinger equation, the quantization phenomena and the physical meaning of wave functions. The book discusses, in a direct and intelligible style, topics of the standard quantum formalism like the dynamical operators and their expected values, the Heisenberg and matrix representation, the approximate methods, the Dirac notation, harmonic oscillator, angular momentum and hydrogen atom, the spin-field and spin-orbit interactions, identical particles and Bose-Einstein condensation etc. Special emphasis is devoted to study the tunneling phenomena, transmission coefficients, phase coherence, energy levels splitting and related phenomena, of interest for quantum devices and heterostructures. The discussion of these problems and the WKB approximation is done using the transfer matrix method, introduced at a tutorial level. This book is a textbook for upper undergraduate physics and electronic engineering students.

We used the theory of finite periodic systems to explain the photoluminescence spectra dependence on the average diameter of nanocrystals embedded in oxide matrices. Because of the broad matrix band gap, the photoluminescence response is basically determined by isolated nanocrystals and sequences of a few of them. With this model we were able to reproduce the shape and displacement of the experimentally observed photoluminescence spectra., 4 pages, 3 figures

We study the space-time evolution of Gaussian electromagnetic wave packets moving through (L/R)n superlattices, containing alternating layers of left and right-handed materials. We show that the time spent by the wave packet moving through arbitrary (L/R)n superlattices are well described by the phase time. We show that in the particular case where the thicknesses dL,R and indices nl,r of the layers satisfy the condition dL|nL| = dRnR, the usual band structure becomes a sequence of isolated and equidistant peaks with negative phase times.

Using the exact two-propagating-modes solutions for electrons in a quasi-2D semiconductor wave guide under sectionally constant magnetic fields and spin-orbit interactions, it is explicitly shown that the Fano-like resonances and antiresonances lead to sudden suppressions and enhancements of the spin-dependent transmission probabilities. Our calculations show that when the magnetic-field-tilting angle θH is increased, the spin-field interaction becomes the most significant mechanism for the spin transitions in magnetic superlattices. Taking advantage of these spin-transport effects, simple and efficient spin-inverter devices are proposed. To better visualize the relative influence of the specific semiconductor properties on the device performance and device characteristics, we consider two magnetic superlattices based on semiconductors having entirely different Lande g-factor: GaAs and InSb. Although slightly more efficient spin-inversion devices are obtained for the GaAs semiconductor, InSb requires lower magnetic fields and its efficiency can be close to 80%.

We present a theory of multichannel disordered conductors by directly studying the statistical distribution of the transfer matrix for the full system. The theory is based on the general properties of the scattering system: flux conservation, time-reversal invariance, and the appropriate combination requirement when two wires are put together. The distribution associated with systems of very small length is then selected on the basis of a maximum-entropy criterion; a fixed value is assumed for the diffusion coefficient that characterizes the evolution of the distribution as the length increases. We obtain a diffusion equation for the probability distribution and compute the average of a few relevant quantities.

We study the relaxation of a degenerate two-level system interacting with a heat bath, assuming a random-matrix model for the system-bath interaction. For times larger than the duration of a collision and smaller than the Poincare recurrence time, the survival probability of still finding the system at timet in the same state in which it was prepared att=0 is exactly calculated.

"The results of a calculation of the phase time as a function of different parameters of the semiconductor layered media to study are presented.Some general features are reported to be present in the tunneling of uncoupled holes for energies above and under the barrier height. Evidencesimilar to that observed for electrons and photons as Hartman predicted for the dependence of the tunneling time with the barrier thicknessis also reported."

We analyze different examples to show that the so-called generalized Hartman effect is an erroneous presumption. The results obtained for electron tunneling and transmission of electromagnetic waves through superlattices and Bragg gratings show clearly the resonant character of the phase time behavior so that a generalized Hartman effect is not expected to occur. A reinterpretation of the experimental results in double Bragg gratings is proposed.