PROPERTIES OF PROPAGATION OF GUIDED ELECTRON WAVES IN COUPLED ASYMMETRIC QUANTUM WELLS

In this article we investigate the properties of the propagation of guided electron waves in the coupled asymmetric quantum wells. By decomposing the eigenfunctions of electron in the coupled double quantum wells in terms of the basis eigenfunctions of the individual wells, the expression of the mode amplitude func-tions for various bare states in wells has been given. By setting up appropriate boundary conditions one can simulate different injecting manners of electron into the system and study how the electron waves trans-fer among various states. The major electron wave transfer happens between the matching bare states in wells. The particular pattern of the transfer depends on the injecting manner and the energy of the inci-dent electron. We also show the influence of the presence of the multimodes on the variatinn of the mode amplitude functions. It leads to producing some oscillations imposed on the original sinusoidal-like func-tions and causing incomplete transfer between a pair of states in channels due to the beating frequency effect or the interference among various modes.     

Preliminary analysis of resonance effect by Helmholtz Schrdinger method

The Helmholtz-Schrdinger method is employed to study the electric field standing wave caused by coupling through a simple slot. There is a good agreement between the numerical results and the resonant conditions presented by the Helmholtz-Schrdinger method. Thus, it can be used in similar cases where the amplitude of the electric field is the important quantity or eigenfunctions of the Schrdinger equation are needed for complicated quantum structures with hard wall boundary conditions.     

Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot

In this paper, the time evolution of the quantum mechanical state of a polaron is examined using the Pekar type variational method on the condition of the electric-LO-phonon strong-coupling and polar angle in RbCl triangular quantum dot. We obtain the eigenenergies, and the eigenfunctions of the ground state, and the first excited state respectively. This system in a quantum dot can be treated as a two-level quantum system qubit and the numerical calculations are performed.The effects of Shannon entropy and electric field on the polaron in the RbCl triangular quantum dot are also studied.     

Topological modes in radiofrequency resonator arrays

Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an experimental and accompanying numerical toolbox to create and analyze topological states in radiofrequency resonator arrays including non-local coupling. These arrays are very easily constructed, offer a variety of geometric configurations, and their eigenfunctions and eigenvalues are amenable to detailed analysis. They offer well defined analogs to coupled oscillator systems in general in that they are characterized by resonances whose frequency spectra depend on the individual resonators, their interactions, and boundary conditions. A comparison of a small one-dimensional experimental system with theory by means of easy to measure S-parameters shows excellent agreement. The numerical toolbox allows for simulations of arbitrarily large systems, revealing an astonishing richness of band structures under systematic parameter variation.     

Electronic transport through superlattice-graphene nanoribbons

In this work, we study quantum transport properties of superlattice-graphene nanoribbons (SGNRs) attached to two semi-infinite metallic armchair graphene nanoribbon (AGNR) leads. The calculations are based on the tight-binding model and Green’s function method, in which localization length, density of states (DOS) and conductance of the system are calculated, numerically. By controlling the layered boron concentration, this kind of system can separate the extended states from the localized states. Our results may have important applications for building blocks in the nano-electronic devices based on GNRs.     

The influence of boundary layer on sound propagation in optical fibers

Physical models of two-layered and three-layered fiber were built. These models were used to calculate acoustic properties of optical fibers. Acoustic properties of fibers with boundary layer and without boundary layer calculated from these model were compared. The propagation of acoustic cylindrical symmetric waves in optical fibers was considered. This problem was treated analytically and numerically in continual approximation. The possibility of simultaneous propagation of two cylindrical symmetric waves in optical fibers with a boundary layer was shown (in a three-layered model). The physical phenomenon of the presence of two waves in the fiber with boundary layer is proposed for study of the boundary layer. Formulas for the calculation of the properties of the boundary layer from the acoustic experiment, verified by numerical calculations, are represented.     

The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach

The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite-dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order q-difference equation (or its degenerate discrete version). In the algebraic sector associated with polynomial eigenfunctions (or their discrete analogues), Bethe equations naturally appear. Beyond this sector, where the Bethe ansatz approach is not applicable in related massive quantum integrable models, the eigenfunctions are also described. The spin-half XXZ open spin chain with general integrable boundary conditions is reconsidered in light of this approach: all the eigenstates are constructed. In the algebraic sector which corresponds to special relations among the parameters, known results are recovered.     

Calculation of matrix elements from eigenenergies: The quartic oscillator

A method is presented whereby matrix elements are derived directly in terms of the eigenenergies and the potential parameters without explicit use of the eigenfunctions. The method consists of determining “initial” matrix elements via quantum mechanical sum rules, and then generating all additional elements through an exact hypervirial recursion relationship. The method is illustrated by sample calculations for the quartic oscillator, and it is shown how one can obtain results more accurate than those computed by direct integration employing numerical eigenfunctions.     

Bound states and band structure—A unified treatment through the quantum Hamilton-Jacobi approach

We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.     

基于FDTD方法的光栅结构光谱特性研究

基于时域有限差分(FDTD)法,从麦克斯韦方程组出发,结合周期边界条件将完全匹配层SAC-PML吸收边界条件应用到所建立的光栅数值模型中.对光栅结构和光滑表面结构的光谱特性进行了数值计算,得到了TM波入射时结构的吸收率,讨论了金属光栅耦合的表面等离子极化(SPPs)和空腔谐振模(Microcavity Mode)现象....     

Rigorous computation of time-dependent electromagnetic fields ingyrotron cavities excited by internal sources

Computation in frequency, as well as in time domain of the electromagnetic field in aperture-coupled cavities which are excited by electron beams, requires an accurate representation of the field. Furthermore, a fast tool for simulation of beam-field interaction in electron tubes is desirable. Application of the modal expansion method, which utilizes both the solenoidal and the irrotational eigenfunctions of the equivalent short-circuited cavity, is generally rigorous but numerically inefficient. In this contribution, three main steps towards a more accurate and simultaneously more efficient analysis are presented. First, it is shown how the irrotational magnetic eigenfunctions can be eliminated from the analysis. Furthermore, some poorly convergent series in the frequency domain analysis as well as in the time-domain analysis are replaced by analytic expressions. Finally, the modal analysis is directly formulated in time domain using rigorous boundary conditions. Numerical results are presented for idealized structures with impressed current density and for self-consistent calculations which are compared to analytical or to numerical results, respectively. Thus, excellent accuracy of the developed method is proved and significant simplifications are justified. For weakly inhomogeneous cavities, the influence of mode conversion on field profile and on numerical aspects is also discussed     

Intersubband optical absorption in two-level quantum wells embedded in a planar microcavity

A theoretical analysis of the optical absorption including both the linear and third-order non-linearity arising from intersubband transitions in two-level quantum wells, which are embedded in a planar microcavity, has been performed. Starting from the Maxwell–Lorentz equations, the expressions of the field in each layer are explicitly given, and the field in the quantum wells is determined via an integral equation, in which the third-order non-linearity is included. Then, by matching the boundary conditions, the field in the quantum-well microcavity structure is rigorously determined, and the absorption coefficient is thus obtained. Detailed numerical calculations show that the optical intersubband absorption can be significantly modified due to the coupling between the quantum wells and the microcavity. This revised version was published online in November 2006 with corrections to the Cover Date.     

Kondo-assistant Aharonov-Bohm transport in a quantum dot-Majorana wire system

We investigate the Kondo-assistant Aharonov-Bohm (AB) transport in a Quantum dot (QD) coupled with a topological Majorana wire. We noted that the conductance exhibits sensitive dependence on the phase factor of AB ring when the wire-QD coupling strength changes. The DOS resonance split when the coupling strength changes from small to large. The current is determined by the Kondo transport characteristics presented by the quantum dots (QDs). Also, the transport results show different p-dependence properties under parallel and anti-parallel leads alignment. We believe that these results can be helpful for understanding the Majorana-QD coupling properties as well as the detection of the Majorana bound states.     

Intermediate wave function statistics

We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred, in the case of star graphs by short (unstable) periodic orbits and, in the case of Seba billiards, by certain families of orbits. We construct sequences of states which have such a limit. Our results are illustrated by numerical computations.     

Dispersion of collective modes at inhomogeneous metal surfaces

A simple model in which electrons are assumed to be specularly reflecting on a plane located a distance u above the boundary of a homogeneous metallic region is proposed for studying dynamical properties of metal surfaces. This model is believed to incorporate essential effects of the inhomogeneity of a pure jellium surface in a new way. It leads to a strong reduction of hydrodynamic dispersion effects for long wavelengths surface plasmons, in agreement with experiment and with various previous calculations. The model is also applied to surface phonons and exact numerical dispersion curves for both surface phonons and plasmons at arbitrary wavelengths are presented.     

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has both integrable and chaotic regions. Examples of the stable and the unstable periodic orbits in the geometry are presented. We numerically solve the biharmonic equation for the flexural vibrations of the Clover shaped plate with clamped boundary conditions. The first few hundred eigenvalues and the eigenfunctions are obtained using a boundary elements method. The Fourier transform of the eigenvalues show strong peaks which correspond to ray periodic orbits. However, the peaks corresponding to the shortest stable periodic orbits are not stronger than the peaks associated with unstable periodic orbits. We also perform statistics on the obtained eigenvalues and the eigenfunctions. The eigenvalue spacing distribution P(s) shows a strong peak and therefore deviates from both the Poisson and the Wigner distribution of random matrix theory at small spacings because of the C_4v symmetry of the Clover geometry. The density distribution of the eigenfunctions is observed to agree with the Porter-Thomas distribution of random matrix theory. Received 12 February 2001 and Received in final form 17 April 2001     

The moment method for boundary layer problems in Brownian motion theory

We apply Grad's moment method, with Hermite moments and Marshak-type boundary conditions, to several boundary layer problems for the Klein-Kramers equation, the kinetic equation for noninteracting Brownian particles, and study its convergence properties as the number of moments is increased. The errors in various quantities of physical interest decrease asymptotically as inverse powers of this number; the exponent is roughly three times as large as in an earlier variational method, based on an expansion in the exact boundary layer eigenfunctions. For the case of a fully absorbing wall (the Milne problem) we obtain full agreement with the recent exact solution of Marshall and Watson; the relevant slip coefficient, the Milne length, is reproduced with an accuracy better than 10^–6. We also consider partially absorbing walls, with specular or diffuse reflection of nonabsorbed particles. In the latter case we allow for a temperature difference between the wall and the medium in which the particles move. There is noa priori reason why our method should work only for Brownian dynamics; one may hope to extend it to a broad class of linear transport equations. As a first test, we looked at the Milne problem for the BGK equation. In spite of the completely different analytic structure of the boundary layer eigenfunctions, the agreement with the exact solution is almost as good as for the Klein-Kramers equation.     

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities are shown to demonstrate nonuniversal correlations due to localization. Varying energy E and mean free path l enable us to experimentally tune from localized to delocalized states. Large level-to-level inverse participation ratio ( I2) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The spatial density autocorrelations of eigenfunctions are shown to spatially decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma models.