The effect of inter-dot separation on the finite difference solution of vertically aligned coupled quantum dots

The effect of inter-dot separation in a double pyramidal vertically aligned quantum dot system is investigated using a finite difference technique. It was found that as the separation distance increased beyond a certain limit, 40 Å in this case, the lowest energy electron wave function was localised in the larger dot. When the dots were in close proximity the probability of the carrier existing in the smaller dot increased. The method used here was a finite difference approach which is widely applicable to many scenarios and provided quantitative results for these intuitive concepts.     

Numerical modeling of the InAs quantum dot with application of coordinate transformation and the finite difference method

In order to resolve the three dimensional Schrödinger equation, we report in this paper a method providing sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum dot. This numerical method, already used in the two-dimensional case, is based on a suitable combination of coordinate transformation and the finite difference method. It provides an efficient and simple approach for the energy and wavefunction calculations of quantum nanostructures. The proposed method is used to investigate the electron and hole energy levels as well as their wave functions in InAs/GaAs strained and unstrained quantum dots with the aim to attain the 1.55 μm wavelength with realistic dot size. The optical transition energies and the oscillator strengths are also studied. The obtained results are in agreement with several previous works.     

Boundary element—dual reciprocity formulation for bound electron states in semiconductor quantum wires

Using the boundary element dual reciprocity method-multi-domain (DRM-MD) a bound electron states and corresponding wave functions in semiconductor quantum wires embedded in a matrix were considered. The single circular and rectangular as well as the two near circular quantum wires were analyzed. In the case of two coupled quantum wires the dependence of the resulting wave function and eigenenergies as a function of the distance between wires was calculated. The DRM-MD gave a linear electron state model and developed numerical approach accurately captured the symmetry breaking and splitting of the degenerated energy states due to presence of additional wire. According to the symmetry of the structures a suitable mesh reduction was employed and different modes were considered separately. For a case of hetero-structures domain decomposition was used.     

The effect of electric field on an asymmetric quantum dot qubit

On the condition of strong electron–LO phonon coupling in an asymmetric quantum dot (QD), we study the eigenenergies and eigenfunctions of the ground and the first excited states under an applied electric field by using variational method of Pekar type. This QD system may be used as a two-level qubit. When the electron is in the superposition state of the ground and the first excited states, we obtain the time evolution of the electron probability density, which oscillates in the QD. It is found that due to the presence of the 3-D anisotropic harmonic potentials in the transverse and longitudinal directions of the QD, the electron probability density shows double-peak configuration, whereas there is only one peak if the confinement is 2-D symmetric in the x- and y-directions. The oscillation period is an increasing function of the transverse and longitudinal effective confinement lengths of the QD, and decreases with respect to the electron–phonon coupling strength and the electric field.     

A model for semiconductor quantum dot molecule based on the current spin density functional theory

Based on the current spin density functional theory, a theoretical model of three vertically aligned semiconductor quantum dots is proposed and numerically studied. This quantum dot molecule (QDM) model is treated with realistic hard-wall confinement potential and external magnetic field in three-dimensional setting. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schrödinger-Poisson system by using the Jacobi-Davidson method and GMRES is given to illustrate the Kohn-Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magnetic field. The Förster-Dexter resonant energy transfer may therefore be generated by two individual QDMs. This may motivate a new paradigm of Fermionic qubits for quantum computing in solid-state systems.     

New numerical method for the eigenvalue problem of the 2D Schrödinger equation

The method consists in a flexible transformation of the 2D problem into a set of 1D single and coupled channel problems. This set of problems is then solved numerically by some highly tuned codes. By choosing codes based on CP methods and formulating an ad-hoc shooting procedure for the localization of the eigenenergies we obtain a version which is very efficient for speed and memory requirements. Extension of the method to more dimensions is also possible.     

Dynamic programming and viscosity solutions for the optimal control of quantum spin systems

The purpose of this paper is to describe the application of the notion of viscosity solutions to solve the Hamilton-Jacobi-Bellman (HJB) equation associated with an important class of optimal control problems for quantum spin systems. The HJB equation that arises in the control problems of interest is a first-order nonlinear partial differential equation defined on a Lie group. Hence we employ recent extensions of the theory of viscosity solutions to Riemannian manifolds in order to interpret possibly non-differentiable solutions to this equation. Results from differential topology on the triangulation of manifolds are then used develop a finite difference approximation method for numerically computing the solution to such problems. The convergence of these approximations is proven using viscosity solution methods. In order to illustrate the techniques developed, these methods are applied to an example problem.     

A quantum-confinement model for surrounding-gate MOSFETS from subthreshold to strong-inversion regions

A new analytical model is developed for quantum-confinement effects of short channel surroundinggate MOSFETs.The eigenenergies and wavefunctions are obtained by solving Schrdinger’s equation with an accurate potential energy distribution.The potential energy distribution is derived from the solution of Poisson’s equation,which contains both depletion charge and free charge.The eigenenergies obtained from our model are compared with other two quantum-confinement models,which use flat-well approximation and parabola-well approximation as the potential energy distributions,respectively.And we point out the relationship between the eigenenergies and the potential energy distribution for the first time.Based on this model,the electron density with quantum confinement effects are derived,and threshold voltage is defined based on average electron density.After considering quantum confinement effects,the electron density becomes smaller while the threshold voltage becomes larger.The results show that this model is applicable from the subthreshold region to the stronginversion region in different channel doping conditions.     

Maskless formation of chromatic-pattern barcodes in two-component microcapsules

We developed a microfluidic method to form chromatic-pattern barcodes without using photomasks as photolithography methods. Two different aqueous quantum dot solutions were loaded as liquid-state cores to form two-component microcapsules, which present as chromatic patterns under UV illumination for barcoding. This microfluidic method highly simplifies the formation of patterns without using any expensive alignment instruments and allows creating the easily discernible pattern-type barcodes with a high coding capacity up to tens of thousands. The easily discernible chromatic-pattern barcodes with a small size down to 40 μm are very promising to conduct multiplexed biomolecular assays under microscopes in general labs.     

Using spectral method as an approximation for solving hyperbolic PDEs

We demonstrate an application of the spectral method as a numerical approximation for solving hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for cases which would be otherwise almost impossible to solve by the more routine methods such as the Finite Difference Method. Eigenvalue problems are included in the class of PDEs that are solvable by this method. Although any complete orthonormal basis can be used, we discuss two particularly interesting bases: the Fourier basis and the quantum oscillator eigenfunction basis. We compare and discuss the relative advantages of each of these two bases.     

Discrete-time quantum walk on the Cayley graph of the dihedral group

The finite dihedral group generated by one rotation and one flip is the simplest case of the non-Abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the dihedral group. Considering the characteristics of the elements in the dihedral group, we conduct the model of discrete-time quantum walk on the Cayley graph of the dihedral group by special coding mode. This construction makes Fourier transformation be used to carry out spectral analysis of the dihedral quantum walk, i.e. the non-Abelian case. Furthermore, the relation between quantum walk without memory on the Cayley graph of the dihedral group and quantum walk with memory on a cycle is discussed, so that we can explore the potential of quantum walks without and with memory. Here, the numerical simulation is carried out to verify the theoretical analysis results and other properties of the proposed model are further studied.     

A robust numerical method for self-polarization energy of spherical quantum dots with finite confinement barriers

By utilizing a novel three-layer dielectric model for the interface between a spherical quantum dot and the surrounding matrix, a robust numerical method for calculating the self-polarization energy of a spherical quantum dot with a finite confinement barrier is presented in this paper. The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest and most widely used step-like model of the dielectric interface, but also completely eliminate the potential numerical divergence which may occur in the Bolcatto-Proetto's formula [P.G. Bolcatto, C.R. Proetto, Partially confined excitons in semiconductor nanocrystals with a finite size dielectric interface, J. Phys. Condens. Matter 13 (2001) 319-334], an approximation method commonly employed for more realistic three-layer dielectric models such as the linear and the cosine-like models frequently mentioned in the literature. Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a three-layer model goes to infinity, an important property that the Bolcatto-Proetto's formula appears not necessarily to possess.     

关于一般耦合矩阵方程的迭代对称解

本文构造了一个有效的迭代方法(CGL)去求解一般耦合矩阵方程的对称解.若一般耦合矩阵方程关于对称解相容,则对于任意给定的初始对称矩阵组,利用所构造的迭代算法,都能在有限步迭代出所求问题的一组对称解,若选用一些特殊的初值,则可获得矩阵方程的极小范数对称解.最后的数值例子表明了所给算法的有效性.     

SMA驱动丝的建模与仿真

研究SMA动力学优化模型,针对形状记忆合金(SMA)驱动丝具有强非线性、迟滞效应等特性,为设计SMA驱动丝的自适应结构,提出建立SMA驱动丝模型并提供高效的仿真方法。采用有限元软件实现了受轴向载荷的SMA驱动丝的仿真建模。对本构模型是根据自由能的一维热-力学耦合模型,可以同时复现形状记忆效应和超弹性。数值仿真能够引起材料相变的非均匀温度和应变分布。仿真结果表明,建立热-力学耦合模型,可为设计SMA驱动丝的自适应结构计算提供可靠依据。     

A numerical method for exact diagonalization of semiconductor quantum dot model

An approach to the exact diagonalization of many-electron Hamiltonian in semiconductor quantum dot (QD) structures is proposed. The QD model is based on 3D finite hard-wall confinement potential and nonparabolic effective-mass approximation (EMA) that render analytical basis functions such as Laguerre polynomials inaccessible for the numerical treatment of this kind of models. In this approach, the many-electron wave function is expanded in a basis of Slater determinants constructed from numerical wave functions of the single-electron Hamiltonian with the nonparabolic EMA which results in a cubic eigenvalue problem from a finite difference discretization. The nonlinear eigenvalue problem is solved by using the Jacobi-Davidson method. The Coulomb matrix elements in the many-electron Hamiltonian are obtained by solving Poisson's problems via GMRES. Numerical results reveal that a good convergence can be achieved by means of a few single-electron basis states.     

Generalized pseudo-Bayes estimation and detection for abruptly changing systems

The problem of state estimation and system-structure detection for linear discrete-time systems with unknown parameters which may switch among a finite set of values is considered. The switching parameters are modeled by a Markov chain with known transition probabilities. Since the optimal solutions require exponentially growing storage and computations with time, a new method of generalized pseudo-Bayes algorithm (GPBA) is proposed to circumvent this problem by using a multi-stage measurement update technique. A minor modification is also presented to correct a defect of the Jaffer and Gupta method. Some simulation comparisons are included to illustrate the effectiveness of the proposed algorithms. It is then shown that, as compared with other GPBAs, a feature of the present GPBA is that it noticeably decreases the size of the required memory when the number of states in the Markov chain is large. The cost to be paid is a slight increase in the computing time.     

Non-Markovian dynamics of quantum coherence of two-level system driven by classical field

In this paper, we study the quantum coherence dynamics of two-level atom system embedded in non-Markovian reservoir in the presence of classical driving field. We analyze the influence of memory effects, classical driving, and detuning on the quantum coherence. It is found that the quantum coherence has different behaviors in resonant case and non-resonant case. In the resonant case, in stark contrast with previous results, the strength of classical driving plays a negative effect on quantum coherence, while detuning parameter has the opposite effect. However, in non-resonant case through a long time, classical driving and detuning parameter have a different influence on quantum coherence compared with resonant case. Due to the memory effect of environment, in comparison with Markovian regime, quantum coherence presents vibrational variations in non-Markovian regime. In the resonant case, all quantum coherence converges to a fixed maximum value; in the non-resonant case, quantum coherence evolves to different stable values. For zero-coherence initial states, quantum coherence can be generated with evolution time. Our discussions and results should be helpful in manipulating and preserving the quantum coherence in dissipative environment with classical driving field.     

含氮碳量子点的电化学制备及其在铜离子检测中的应用

碳量子点作为一种新型的碳纳米荧光材料,由于其具有生物相容性好等优点而备受关注。该文以乙二胺为原料,通过电化学方法,制备了一种含氮碳量子点。该含氮碳量子点,同时具有单光子和双光子荧光响应特性,且耐光漂白和pH稳定。利用Cu2+对所制备的含氮碳量子的荧光淬灭特性于离子检测的试验表明,该含氮碳量子点可用于微量Cu2+的定量分析。     

Multidimensional exponentially fitted simplicial finite elements for convection-diffusion equations with tensor-valued diffusion

Abstract In this paper we propose and analyze an exponentially fitted simplicial finite element method for the numerical approximation of solutions to diffusion-convection equations with tensor-valued diffusion coefficients. The finite element method is first formulated using exponentially fitted finite element basis functions constructed on simplicial elements in arbitrary dimensions. Stability of the method is then proved by showing that the corresponding bilinear form is coercive. Upper error bounds for the approximate solution and the associated flux are established.