Diffusion in a bistable potential

The problem of diffusion of a particle in a bistable potential is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. The potential is modeled as two parabolic wells separated by a parabolic barrier. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in one of the wells. In the limit of a high barrier the rate of transition to the other well is given by an asymptotic result due to Kramers. For a potential barrier of moderate height there are significant corrections to the asymptotic result.     

Tunneling in double-barrier ZnSe/ZnTe structures — time-dependent analysis

Wave-packet time-dependent quantum mechanics is used to calculate the tunneling probability through a double-barrier ZnSe/ZnTe structure. The time-dependent transmission characteristics are obtained for several structures, and detailed electron dynamics is presented. The resonant peaks due to the presence of the discrete energy levels in the quantum well as well as in the barrier region are observed.     

The effect of periodic magnetic-electric barriers on electron transport in a nanostructure

Using the transfer matrix method, the transmission probability, the spin polarization and the electron conductance of a ballistic electron are studied in detail in a nanostructure. We observe that these quantities sensitively depend on the number of periodic magnetic-electric barriers. As the number of periods increases, the resonance splitting increases, the number of the resonance peaks increases and the peaks become sharper as well as the spin polarization being enhanced. Surprisingly, a polarization of nearly 100% can be achieved by spin-dependent resonant tunneling in this structure, although the average magnetic field of the structure is zero.     

Velocity fluctuations of a column of water streaming down a wire: the possibility of one-dimensional turbulence

In this paper we study the influence of the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron on transmission features in single barrier structures. Within the parabolic conduction-band approach, a modified one-dimensional effective-mass Schr?dinger equation, including the magneto-coupling effect generated from the position-dependent effective mass of the electron, is strictly derived. Numerical calculations for single barrier structures show that the magneto-coupling effect brings about a series of the important changes for the transmission probability, the above-barrier quasi-bound states, and the tunneling time. Through examining the variation of the above-barrier resonant-transmission spectrum with the barrier width and observing the well-defined Lorentzian line-shape of the above-barrier resonant peaks, we convincingly show that the above-barrier resonant transmission in single barrier structures is delivered by the above-barrier quasibound states in the barrier region, just as the below-barrier resonant tunneling in double barrier structures is mediated by the below-barrier quasi-bound states in the well. Furthermore, we come to the conclusion that the magneto-coupling effect brings about not only the splitting of the above-barrier quasi-bound levels but also the striking reduction of the level-width of the quasi-bound states, correspondingly, the substantial increase of the density of the quasi-bound states. We suggest that magneto-coupling effects may be observed by the measurements of the optical absorption spectrum associated with the above-barrier quasi-bound states in the single barrier structures. Received: 26 September 1997 / Revised: 26 November 1997 / Accepted: 15 December 1997     

Diffusion and convection after escape from a potential well

The escape by diffusion of a particle from a potential well in one dimension is strongly influenced by the application of a field in the adjacent half-space. At long times the probability distribution becomes a uniformly moving and steadily broadening gaussian in this half-space. The mean time of escape from the well is given by a simple expression in terms of the mean first passage time and the coefficient of the long-time tail in the occupation probability of the well in the absence of the field. Transient effects in space and time are studied in explicit form for a parabolic potential well.     

Transmission resonances in magnetic-barrier structures

Quantum transport properties of electrons in simple magnetic-barrier (MB) structures and in finite MB superlattices are investigated in detail. It is shown that there exists a transition of transmission resonances, i.e., from incomplete transmission resonances in simple MB structures consisting of unidentical blocks, to complete transmission resonances in comparatively complex MB structures (, n is the number of barriers). In simple unidentical block arrangements in double- and triple-MB structures we can also obtain complete transmission by properly adjusting parameters of the building blocks according to k_y-value (k_y is the wave vector in y direction). Strong suppression of the transmission and of the conductance is found in MB superlattices which are periodic arrangements of two different blocks. The resonance splitting effect in finite MB superlattices is examined. It is confirmed that the rule (i.e., for n-barrier tunneling the splitting would be (n-1)-fold) obtained in periodic electric superlattices can be extended to periodically arranged MB superlattices of identical blocks through which electrons with tunnel, and it is no longer proper for electrons with k _y <0 to tunnel. Received: 18 August 1997 / Revised: 20 September 1997 / Accepted: 13 October 1997     

Solitary self-gravitational potential in magnetized astrophysical degenerate quantum plasmas

A rigorous theoretical investigation has been conducted on solitary self-gravitational potential structures in a magnetized degenerate quantum plasma system (containing heavy nuclei and degenerate electrons). The reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV) equation, which admits a solitary wave solution for small but finite amplitude limit. It has been shown, for the first time, that the periodic U-shaped structures represented by secant square function [Asaduzzaman et al, Physics of Plasmas, 24 , 052102 (2017)] are converted into solitary self-gravitational potential structures represented by hyperbolic secant square function due to the presence of a static external magnetic field. It is also observed that the effects of the static external magnetic field and obliqueness significantly modify the basic properties (viz. amplitude, width, speed, etc.) of the solitary self-gravitational potential structures.     

双量子阱中光子辅助电子自旋隧穿

采用单电子有效质量近似理论, Floquet理论和传递矩阵方法, 对包含时间周期场的双量子阱中单电子的自旋隧穿特性进行了研究, 对InP/InAs半导体材料进行了数值计算. 重点研究了Rashba型和Dresselhaus型自旋轨道耦合、量子阱结构以及偏压对电子隧穿的影响. 这些结果可以为设计和调控半导体自旋电子器件提供一定的理论依据. 关键词： 光子辅助隧穿 隧穿概率 量子阱     

Multimode network analysis for dielectric leaky-wave antennas consisting of multilayer periodic structure with arbitrary dielectric distributions

The multimode network method is used to analyze the radiation characteristics of the leaky-wave antenna consisting of multilayer dielectric periodic structure with arbitrary dielectric distributions in each layer. The eigenfunction of each periodic layer is determined by Floquet theorem; and the mode matching combining with generalized transverse resonant method are used to derive the dispersion equation of the leaky-wave antenna. The complex transmission constant is calculated by Newton iterative method and the radiation characteristics of the antenna are obtained. Some antenna structures are analyzed and useful guidelines for design of the leaky-wave antennas are suggested.     

Escape by diffusion from a square well across a square barrier

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.     

周期势场中电子的中心方程及其应用

周期势场中电子的薛定谔微分方程变换为K空间的称为中心方程的线性齐次方程组，利用此方程可以证明布洛赫定理，讨论弱周期势场中电子的能带。     

Monte Carlo method for the Schrödinger equation with an asymmetric periodic potential

A new numerical method is proposed for solving the Cauchy problem for the Schrödinger equation with an asymmetric periodic potential superimposed by a constant electric field. The solution to the Cauchy problem is used to determine the electron’s mean momentum as a function of time, initial conditions, and the applied field. Given an initial state, the mean momentum characterizes the mean current and the conductivity of an asymmetric periodic structure known as the ratchet potential.     

Chaotic diffusion for particles moving in a time dependent potential well

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and; (ii) by the solution of the diffusion equation. The dynamic of the diffusing particles is made by the use of a two dimensional, nonlinear area preserving map for the variables energy and time. The phase space of the system is mixed containing both chaos, periodic regions and invariant spanning curves limiting the diffusion of the chaotic particles. The chaotic evolution for an ensemble of particles is treated as random particles motion and hence described by the diffusion equation. The boundary conditions impose that the particles can not cross the invariant spanning curves, serving as upper boundary for the diffusion, nor the lowest energy domain that is the energy the particles escape from the time moving potential well. The diffusion coefficient is determined via the equation of the mapping while the analytical solution of the diffusion equation gives the probability to find a given particle with a certain energy at a specific time. The momenta of the probability describe qualitatively the behavior of the average energy obtained by numerical simulation, which is investigated either as a function of the time as well as some of the control parameters of the problem.     

Persistent current and transmission probability in the Aharonov-Bohm ring with an embedded quantum dot

Persistent current and transmission probability in the Aharonov-Bohm (AB) ring with an embedded quantum dot (QD) are studied using the technique of the scattering matrix. For the first time, we find that the persistent current can arise in the absence of magnetic flux in the ring with an embedded QD. The persistent current and the transmission probability are sensitive to the lead-ring coupling and the short-range potential barrier. It is shown that increasing the lead-ring coupling or the short-range potential barrier causes the suppression of the persistent current and the increasing resonance width of the transmission probability. The effect of the potential barrier on the number of the transmission peaks is also investigated. The dependence of the persistent current and the transmission probability on the magnetic flux exhibits a periodic property with period of the flux quantum.     

Equivalent circuit of the barrier-conductor structures

Novel heterostructure devices are comprised of potential barriers connected by short conductors. In this paper we present a simple theory for the transport properties of the barrier-conductor chain. The analysis is based on the solution of the Boltzmann equation supplemented by the boundary conditions provided by the barrier reflection and transmission probabilities. As an application of the theory the small signal equivalent circuit is constructed for the single and double barrier cases and for the infinite periodic chain. The high frequency properties of these structures are discussed. In general, the multibarrier structures show transit time resonances associated with multiple reflections.     

Electronic transport for armchair graphene nanoribbons with a potential barrier

This paper studies the electronic transport property through a square potential barrier in armchair-edge graphene nanoribbon (AGNR). Using the Dirac equation with the continuity condition for wave functions at the interfaces between regions with and without a barrier, we calculate the mode-dependent transmission probability for both semiconducting and metallic AGNRs, respectively. It is shown that, by some numerical examples, the transmission probability is generally an oscillating function of the height and range of the barrier for both types of AGNRs. The main difference between the two types of systems is that the magnitude of oscillation for the semiconducting AGNR is larger than that for the metallic one. This fact implies that the electronic transport property for AGNRs depends sensitively on their widths and edge details due to the Dirac nature of fermions in the system.     

Revealing macrodefects in periodic structures of the transmission type in white light on the basis of shift of images

The possibility of revealing macrodefects in periodic structures of the transmission type in white light on the basis of shift of images of the structures under investigation is shown. A simple scheme of visualization of macrodefects on the basis of obtaining shifted images of structures by using a plane mirror placed behind the periodic structure is described. A method for revealing macrodefects in periodic structures with the possibility of increasing the sensitivity of measurements is proposed. The method is based on making a photograph of a periodic structure with subsequent optical processing of this structure and its photograph, which are optically conjugate and shifted with respect to each other. An increase in the sensitivity of this method is achieved owing to separation of complex conjugate orders of diffraction of light by the structure and its photograph. The methods proposed do not require using reference periodic structures. Experimental results of testing of the methods for visualization of macrodefects in cross-shaped metal grids are presented.     

Resonant tunneling in periodic multiple-barrier structures with compound-barrier unit

Resonant tunneling in multiple-barrier structures with arbitrary potential profile is studied theoretically. Analytical expressions of the transmission coefficient and the resonance condition are derived by taking into account the mass difference between well and barrier layers. The basic barrier unit in the periodic multiple-barrier structure may be a compound-barrier structure, and the simplest compound-barrier unit is the double-barrier unit. Two independent resonance conditions exist in the multiple-barrier structures with compound-barrier unit and both the subband gap energy and the energy value at the center of the subband gap may be determined analytically and independently for the multiple-barrier structure with double-barrier unit.     

A three-dimensional frequency selective structure based on the modes coupling of spoof surface plasmon and waveguide transmission

A three-dimensional frequency selective structure (3D FSS) was proposed by applying the spoof surface plasmon (SSP) structures into periodic waveguides, which realizes an enhanced broadband transmission in low frequencies, below the cut-off frequency of periodic waveguides. The transmission characteristics of SSP structures and periodic waveguides as well as their coupling modes are investigated by simulation and experiment method. According to our analysis, the pass-band of this 3D FSS can be customized through changing the values of structure parameters and it also has a good angular stability. In addition, this paper also provides a simple assembly plan for sample preparation. This proposal may be useful for improving filtering performances and gives an effective approach for designing 3D FSSs.     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.