Transmission characteristics including the coupling effect between normal and lateral degrees of freedom in single barrier structures with a longitudinal magnetic field

Within the parabolic conduction-band approach, a modified one-dimensional effective mass Schrödinger equation, including the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron, is strictly derived. This magneto-coupling effect is generated from the space-dependent effective mass of the electron. Numerical calculations for single barrier structures show that the magneto-coupling has a series of important effects on the transmission probability and the above-barrier quasi-bound states. We suggest that the magneto-coupling effect may be observed by measurements of the optical absorption spectrum in the single barrier structures.     

Spin-flip conductance and magnetoresistance of magnetic nanocontacts

The quantized conductance of nanocontacts with atomic sizes is calculated with allowance made for the conduction-electron spin flip in terms of the quantum scattering theory. The exact solution of the Schrödinger equation describing the electron motion in a piecewise-smooth potential is used as the zeroth-order approximation of the perturbation theory. The probabilities of electron transmission (reflection) through a magnetic domain wall, as well as the spin-conserving and spin-flip conductances of the nanocontact, are calculated. It is demonstrated that the spin-flip conductance imposes the natural limitation on the formally infinite increase in the ballistic magnetoresistance of the nanocontact when its cross-sectional area tends to zero.     

Quantum-mechanical substantiation of a similar change in the kinetic energy component of an electron along the magnetic field within each Landau level

A detailed solution to the Schr?dinger equation for an electron in the presence of a quantizing magnetic field is considered using the method of separation of variables. The discrete energy levels occurring in this case are regarded as the potential barriers of finite height, with an electron moving normal to them along the magnetic-field direction. A similar change in the difference between the energy values within the neighboring Landau levels allows us to show, basing on the general properties of one-dimensional electron motion in the magnetic field, that within each quantum energy level, the kinetic-energy component of a longitudinal electron motion continuously is varied between 0 and 2μ_BH, whereas the probability density of particle location is practically damped into the potential-barrier depth as it moves along the magnetic-field direction. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–7, October, 2006.     

电子横向运动对共振隧穿的影响

讨论了电子横纵方向运动耦合时的隧穿现象,对CdSe/Zn1-xCdxSe方形双势垒结构和抛物形双势垒结构的数值计算表明,在零偏压和非零偏压情况下,电子横向运动对共振隧穿的影响是不容忽略的。     

Energy relaxation of electrons impacts on channel quantization in nano-MOSFETs

The effects of the rising electron temperature due to the energy relaxation on the quantization of the inversion layer in a nano-metal–oxide–semiconductor field transistor (MOSFET) with p-type silicon substrate have been theoretically investigated via self-consistent solution to the coupled Schrödinger equation with considering quantum coupling effects and Poisson equation. The first quantized energy level in the inversion layer rises from 3.6 to 211.4 %, and the total number of the inversion channel electron decreases from 95.7 to 6.5 % relative to those neglecting energy relaxation of channel electrons when the channel electric field increases from 10 to 55 kV/cm. The output characteristic of MOSFET will be largely affected by the energy relaxation when the channel electric field is higher than 10 kV/cm. All these suggest that the energy relaxation of channel electrons should be considered in the modeling of MOSFETs for higher channel electric field.     

Landau diamagnetism and determination of the longitudinal and transverse kinetic energy components of a degenerate nonrelativistic electron gas

The Fermi energy, average total kinetic energy density, and also average kinetic energy of finite diamagnetic motion of an electron gas of specified concentration are calculated. The kinetic energy of continuous longitudinal motion of the electrons along the direction of an external magnetic field H is determined. It is found that in the quantum limit, when the maximum Landau quantum number N _m =0, the kinetic energy of continuous longitudinal motion tends to zero with increase in the external magnetic field strength. If the maximum Landau quantum number is greater than zero, the longitudinal and transverse kinetic energy components of the degenerate electron gas change only insignificantly. Byelorussian State University; Brest State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 31–35, July, 1999.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Slow light beam splitter

We demonstrate a slow light beam splitter using rapid coherence transport in a wall-coated atomic vapor cell. We show that particles undergoing random and undirected classical motion can mediate coherent interactions between two or more optical modes. Coherence, written into atoms via electromagnetically induced transparency using an input optical signal at one transverse position, spreads out via ballistic atomic motion, is preserved by an antirelaxation wall coating, and is then retrieved in outgoing slow light signals in both the input channel and a spatially-separated second channel. The splitting ratio between the two output channels can be tuned by adjusting the laser power. The slow light beam splitter may improve quantum repeater performance and be useful as an all-optical dynamically reconfigurable router.     

Universal invariants in quantum mechanics and physics of optical and particle beams

We give a brief review of the theory of quantum universal invariants and their counterparts in the physics of light and particle beams. The invariants concerned are certain combinations of the second- and higher-order moments (variances) of quantum-mechanical operators, or the transverse phase-space coordinates of the paraxial beams of light or particles. They are conserved in time (or along the beam axis) independently of the concrete form of the coefficients of the Schrödinger-like equations governing the evolution of the systems, provided that the effective Hamiltonian is either a generic quadratic form of the generalized coordinate-momenta operators or a linear combination of generators of some finite-dimensional algebra (in particular, any semisimple Lie algebra). Using the phase space representation of quantum mechanics (paraxial optics) in terms of the Wigner function, we elucidate the relation of the quantum (optical) invariants to the classical universal integral invariants of Poincaré and Cartan. The specific features of Gaussian beams are discussed as examples. The concept of the universal quantum integrals of motion is introduced, and examples of the “universal invariant solutions” to the Schrödinger equation, i.e., self-consistent eigenstates of the universal integrals of motion, are given.     

Mesoscopic spin Hall effect

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is short compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average.     

Quantum transport andI–Vcharacteristics of quantum size field effect transistor

Quantum electron transport is expected to occur in nanometer-size field effect transistors. We show that the amplitude of the transmitted wave equals 1 only when the electric field in the conducting channel is zero. By reducing the dimension of the quantum transport from bulk to a two-dimensional electron gas system, and further to a one-dimensional quantum wire, the current-bias relation is not affected while the gate control over the drain current weakens. Starting from the Poisson and Schrödinger equations, we have studied numerically the quantum wave transport through the conduction channel where scattering processes are neglected, theI–Vcharacteristic of a typical heterojunction high electron mobility transistor shows a linear relationship between drain current and voltage at low drain bias, but the drain current decreases with increasing drain voltage at a high bias.     

Acoustic activity effect for picosecond soliton-like pulses

A theoretical analysis is made of the acoustic activity for interfering picosecond acoustic soliton-like pulses of down to a single oscillation period. An analysis is made of the case where these pulses propagate parallel to an external magnetic field and one of the acoustic axes in a cubic crystal containing paramagnetic impurities having effective spin S = 1. Allowance is made for natural, magnetic (Faraday), and cross acoustic activity. This cross activity is caused by the significant spatial nonlocality of the spin-phonon interaction for such short pulses in crystals having no center of inversion in the presence of paramagnetic impurities. A system of nonlinear equations is obtained for the transverse and longitudinal components of the strain in the form of a coupling between the “differentiated” nonlinear Schrödinger equation (with nonlinearity after the derivative sign) and the Korteweg-de Vries equation which generalizes the known systems of long-short-wavelength resonance to the case where the slowly varying envelope approximation is not valid. An approximate solution of this system is used to study the structure of an elastic soliton-like pulse whose transverse component has a rotating plane of polarization, which propagates under conditions of nonlinear coupling with the longitudinal strain.     

Factorizing coupled quantum systems and damped nonlinear Schrödinger equations

We show that the wave function of a coupled quantum system may factorize for certain coupling operators, resulting in wave functions and effective nonlinear Hamiltonians for the subsystems. Systems of coupled harmonic oscillators with discrete or continuous spectra are considered, where all degrees of freedom move in time-dependent coherent Glauber states.We present the general formalism and study two examples in detail. The problem of radiation damping results under drastic assumptions in exponentially damped harmonic motion, obeying a nonlinear Schrödinger equation. In the second example, a different type of coupling is studied which yields inverse power law damping.     

Landau Diamagnetism,Pauli Paramagnetism,and Determination of Longitudinal and Transverse Kinetic Energy Components of a Degenerate Nonrelativistic Electron Gas

The Fermi energy, density of average kinetic energy, and average density of kinetic energy of the transverse finite motion of an electron gas of a specified concentration are calculated taking into account Landau diamagnetism and Pauli paramagnetism. The kinetic energy of a longitudinal continuous electron motion along the direction of the external magnetic field H is estimated. It is shown that the kinetic energy of the longitudinal continuous motion vanishes with increase in the external magnetic field strength in the quantum limit where the maximum Landau quantum number N _m = 0. For N _m > 0, the longitudinal kinetic energy component of a degenerate electron gas somewhat increases with magnetic field strength. The cause of the erroneous result is discussed.     

Non-Markovian weak coupling limit of quantum Brownian motion

We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a harmonic oscillator interacting with a squeezed thermal bath. This equivalence guarantees preservation of positivity of the density operator during the time evolution and allows one to establish a connection between the dynamics of Schrödinger cat states in squeezed environments and environment-induced decoherence in quantum Brownian motion.

     

Pseudo-invariant Eigen-Operator for Deriving Energy-Level Gap for Quantum Bit in Quantum Circuit

Based on the method of pseudo invariant eigenoperator (PIEO), a fully quantum mechanical scheme is investigated for the coupling between a rf SQUID qubit and an off-resonance quantized single-mode electromagnetic field in the strong coupling regime. In order to derive the systematic energy-level gap obtained by the pseudo-invariant operator of the quantum system, we give operation props for corresponding quantum manipulation. In comparison with the solution of stationary Schrödinger equation, the PIEO method could be quite concise and effective to obtain energy-level gap for the given system.     

Phase control of Goos-Hänchen shifts in a four-level quantum dot nanostructure

In this letter, phase control of the Goos-Hänchen shifts of the reflected and transmitted probe light beams through a cavity containing four-level InGaN/GaN quantum dot nanostructure is theoretically discussed. In order to achieve the wave functions and their corresponding energy levels of the mentioned quantum dot nanostructure, Schrödinger and Poisson equations must be solved in a self consistent manner for carriers (here electron) in quantum dot. It is found that the coupling field, the pumping field as well as the cycling field can enhance the GH shifts of the reflected and transmitted probe beams. The effect of relative phase and the detuning of the probe light on the GH shifts of the reflected and transmitted probe beams are also investigated. We find that the GH shifts can be switched between the large positive and negative values by adjusting the controllable parameters.     

Localization on Quantum Graphs with Random Vertex Couplings

We consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. We obtain necessary conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges.