Path integral for Koenigs spaces

I discuss a path-integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short “Koenigs spaces”. Their construction is simple: one takes a Hamiltonian from a two-dimensional flat space and divides it by a two-dimensional superintegrable potential. These superintegrable potentials are the isotropic singular oscillator, the Holt potential, and the Coulomb potential. In all cases, a nontrivial space of nonconstant curvature is generated. We can study free motion and the motion with an additional superintegrable potential. For possible bound-state solutions, we find in all three cases an equation of the eighth order in the energy E. The special cases of the Darboux spaces are easily recovered by choosing the parameters accordingly. The text was submitted by the authors in English.     

Path integration on Darboux spaces

In this paper, the Feynman path integral technique is applied to two-dimensional spaces of nonconstant curvature: these spaces are called Darboux spaces D _I-D _IV. We start each consideration in terms of the metric and then analyze the quantum theory in the separable coordinate systems. The path integral in each case is formulated and then solved in the majority of cases; the exceptions being the quartic oscillators where no closed solution is known. The required ingredients are the path integral solutions of the linear potential, the harmonic oscillator, the radial harmonic oscillator, the modified Pöschl-Teller potential, and the spheroidal wave functions. The basic path integral solutions, which appear here in a complicated way, have been developed in recent work and are known. The final solutions are represented in terms of the corresponding Green’s functions and the expansions into the wave functions. We also sketch some limiting cases of the Darboux spaces, where spaces of constant negative and zero curvature emerge.     

Calculation of the intensity of Touschek electrons in the VEPP-4M storage ring

Formulas for calculating the intensity of intrabeam scattering of electrons in the Born approximation for the one- and two-dimensional collision models have been obtained for the nonrelativistic and relativistic cases. The Baier-Katkov-Strakhovenko two-dimensional relativistic model with Coulomb corrections has been analyzed. Formulas in the ultrarelativistic limit have been obtained using this model. Different models have been compared. The intensities of Touschek electrons and the polarization contribution have been calculated under the conditions of the detection of scattered particles at the VEPP-4M storage ring. The calculations have been compared to experimental data.     

Two-Dimensional Linear Dependencies on the Coordinate Time-Dependent Interaction in Relativistic Non-Commutative Phase Space

In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time-dependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis-Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.     

基于硅锗异质结的二维量子点阵列的制备与表征

硅基半导体量子点中的自旋量子比特近几年来发展迅速,其单比特门与两比特门操作保真度已经突破了容错量子计算的阈值.在此基础上,如何构建硅基量子点二维阵列变得广受学界关注,然而二维阵列复杂的结构在器件制备和测量上均带来挑战.本文设计并成功制备了一种Si/SiGe异质结上的2×4结构八量子点二维阵列器件.借助输运测量方法测量了八量子点器件的全部电荷稳定性相图,并进一步地使用电荷感应调制测量方法得到了器件内的少电子区电荷稳定性相图,说明了对量子点电荷态的高灵敏度探测能力.此外,通过调控势垒电极展示了对量子点间隧穿耦合的调控作用并测量了多量子点耦合的电荷稳定性相图.本文的研究结果展示了使用Si/SiGe异质结构建自旋量子比特二维阵列的潜力,为未来硅量子点二维阵列的进一步扩展提供经验与参考.     

二维谐振子与加反平方势的二维氢原子的能量关系

通过SU(1,1)代数,找出了二维谐振子与加上反平方势微扰后的二维氢原子的能量对应关系     

A physics-based potential and electric field model of a nanoscale rectangular high-K gate dielectric HEMT

In this paper, we have developed a physics-based model for surface potential, channel potential, electric field and drain current for AlGaN/GaN high electron mobility transistor with high-K gate dielectric using two-dimensional Poisson equation under full depletion approximation with the inclusion of effect of polarization charges. The accuracy of the model has been verified and is found to be in good agreement with the simulated results.     

Optimal lattice configurations for interacting spatially extended particles

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and the mass concentration depends on the density we have fixed. In the second case, both interacting potential and density of the distribution of mass are described by completely monotone functions in which case the optimality holds at any fixed density.     

Plasmon mechanism of resistance magnetooscillations in a two-dimensional electron system in strong electric fields

A multielectron approach is developed to explain the resistance magnetooscillations in two-dimensional electron systems that have recently been detected under the action of microwave pumping [1] or a strong dc electric field [23]. A qualitative change in the screened impurity potential in a strong electric field is taken into account for the first time. When considered in the rest frame of the center of the cyclotron orbit, the impurity potential becomes nonstationary and, thus, should be screened dynamically. This fact substantially changes the picture of impurity scattering in a “pure” two-dimensional system: a dissipative current is induced by the excitation of two-dimensional plasmons rather than by one-electron transitions between the Landau levels. In the case of microwave pumping, every period of resistance oscillation in a reciprocal magnetic field is formed by the excitation of the corresponding magnetoplasmon branch, and the fine structure of oscillations is formed by the singularities of the magnetoplasmon density of states. In a “dirty” two-dimensional system, the role of electron-electron interaction weakens, collective excitations cease to exist, and the results transform into the well-known results obtained in terms of a one-electron approach.     

二维环状无限深势阱中的朗道能级

对于带电粒子在磁场中的运动,在各种教科书上都有详细的阐述,但是对于限制在二维无限深势阱的带电粒子,现在流行的各种量子力学教科书上都没有阐述.本文主要讨论二维无限深势阱中的能级和朗道能级.     

The phase diagram of the 2D Ising model with anisotropic next-nearest-neighbor and four-spin interactions

In the present paper, the two-dimensional Ising model with anisotropic nearest-neighbor, next-nearest-neighbor and four-spin interactions has been studied. The ground states and energy of the model have been obtained. The model is equivalent to an eight-vertex model on its dual lattice. In some special cases, the model can be solved exactly as a zero-field eight-vertex model or a free-fermion model. Explicit phase diagrams are obtained exactly.     

A class of two dimensional models with extended structure solutions

We study some properties of a class of two-dimensional models which have infinite dimensional groups of symmetry which include both the Euclidean and Minkowskian groups. We show that all solutions of these models are self-dual and correspond to mappings of the 2 dimensional plane into itself which locally preserve the area. When treated as candidates for soliton-like structures we see that the structures are localised. In most cases the energy density of these structures has a power-like tail; in some cases, e.g. the modified sine-Gordon model, the localisation is exponential.     

Metastable resistance-anisotropy orientation of two-dimensional electrons in high Landau levels

In half-filled high Landau levels, two-dimensional electron systems possess collective phases which exhibit a strongly anisotropic resistivity tensor. A weak, but as yet unknown, rotational symmetry-breaking potential native to the host semiconductor structure is necessary to orient these phases in macroscopic samples. Making use of the known external symmetry-breaking effect of an in-plane magnetic field, we find that the native potential can have two orthogonal local minima. It is possible to initialize the system in the higher minimum and then observe its relaxation toward equilibrium.     

A two-dimensional vibration analysis of piezoelectrically actuated microbeam with nonideal boundary conditions

In this paper, the influences of nonideal boundary conditions (due to flexibility) on the primary resonant behavior of a piezoelectrically actuated microbeam have been studied, for the first time. The structure has been assumed to treat as an Euler–Bernoulli beam, considering the effects of geometric nonlinearity. In this work, the general nonideal supports have been modeled as a the combination of horizontal, vertical and rotational springs, simultaneously. Allocating particular values to the stiffness of these springs provides the mathematical models for the majority of boundary conditions. This consideration leads to use a two-dimensional analysis of the multiple scales method instead of previous works' method (one-dimensional analysis). If one neglects the nonideal effects, then this paper would be an effort to solve the two-dimensional equations of motion without a need of a combination of these equations using the shortening or stretching effect. Letting the nonideal effects equal to zero and comparing their results with the results of previous approaches have been demonstrated the accuracy of the two-dimensional solutions. The results have been identified the unique effects of constraining and stiffening of boundaries in horizontal, vertical and rotational directions. This means that it is inaccurate to suppose the nonideality of supports only in one or two of these directions like as previous works. The findings are of vital importance as a better prediction of the frequency response for the nonideal supports. Furthermore, the main findings of this effort can help to choose appropriate boundary conditions for desired systems.     

Progress in functional studies of transition metal borides

In recent years, transition metal borides (TMBs) have attracted much attention because they are considered as potential superhard materials and have more abundant crystal structures compared with traditional superhard materials. So far, however, no superhard materials have been found in TMBs. A large number of structures and potential new properties in TMBs are induced by the various hybridization ways of boron atoms and the high valence electrons of transition metals, which provide many possibilities for its application. And most TMBs have layered structures, which make TMBs have the potential to be a two-dimensional (2D) material. The 2D materials have novel properties, but the research on 2D TMBs is still nearly blank. In this paper, the research progress of TMBs is summarized involving structure, mechanical properties, and multifunctional properties. The strong covalent bonds of boron atoms in TMBs can form one-dimensional, two-dimensional, and three-dimensional substructures, and the multiple electron transfer between transition metal and boron leads to a variety of chemical bonds in TMBs, which are the keys to obtain high hardness and multifunctional properties of TMBs. Further research on the multifunctional properties of TMBs, such as superconductors, catalysts, and high hardness ferromagnetic materials, is of great significance to the discovery of new multifunctional hard materials.     

A class of partially solvable two-dimensional quantum models with periodic potentials

The supersymmetric approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lamé, associated Lamé, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lamé potential) obeys the property of self-isospectrality.     

Contactless measurement of the conductivity of two-dimensional electrons in the regime of microwave-induced giant magnetoresistance oscillations

Magnetic-field dependences of the conductivity of a two-dimensional electron system obtained by contact and contactless measurements in the regime of microwave-induced giant magnetoresistance oscillations have been comparatively analyzed. The contactless technique for studying the conductivity of two-dimensional electrons is based on measuring the attenuation of the RF signal propagating along a coplanar waveguide manufactured using lithography on the sample surface. It has been found that Shubnikov-de Haas oscillations of conductivity are observed in both techniques, whereas the microwave-induced giant magnetoresistance oscillations appear only in the contact measurements. This contradiction indicates that the contact and/or boundary regions of the two-dimensional system with a strong potential gradient play an important role for the observation of the induced magnetoresistance oscillations.     

Spatial condensation of trapped polaritons in graphene and semiconductor structures

The theoretical and experimental status of the Bose–Einstein Condensation (BEC) of trapped quantum well (QW) polaritons in a microcavity is presented. The results of recent experiments that have shown the possibility to create an in-plane harmonic potential trap for a two-dimensional (2D) exciton polaritons in a cavity are discussed. We report the theory of BEC and of the trapped QW exciton polaritons in a microcavity. In addition, we study the BEC of trapped magnetoexciton polaritons in a graphene layer (GL) embedded in an optical microcavity in high magnetic field. In both cases the polaritons are considered to be in a harmonic potential trap. We compare the theoretical results with the existing experiments and discuss the experimental observation of predicted phenomena.     

柱形分布的电荷产生的电势

将无限长线电荷看成二维平面上的一个“源”,利用电势叠加原理计算了无限长柱形均匀分布的电荷产生的电势.这些柱体的截面电荷分布包括可解析表示和不可求解表示两种,后者可以通过数值计算给出结果.因此这种方法实际上可以计算任意截面柱形电荷分布的电势.通过计算,展示了各种电荷分布所产生电场的特性和共同特征.