Effect of the number of defect particles on the structure and dispersion relation of a two-dimensional dust lattice system

The effect of the number of defect particles on the structure and dispersion relations of a two-dimensional (2D) dust lattice is studied by molecular dynamics (MD) simulation. The dust lattice structures are characterized by particle distribution, nearest neighbor configuration and pair correlation function. The current autocorrelation function, the dispersion relation and sound speed are used to represent the wave properties. The wave propagation of the dust lattice closely relates to the lattice structure. It shows that the number of defect particles can affect the dust lattice local structure and then affect the dispersion relations of waves propagating in it. The presence of defect particles has a greater effect on the transverse waves than on the longitudinal waves of the dust lattice. The appropriate number of defect particles can weaken the anisotropy property of the lattice.     

Ewald's dynamical theory of diffraction for a defect crystal

The paper is based on the Ewald's approach to the problem of interaction of an electromagnetic wave with a coulomb crystal lattice. Born's formalism of the crystal dynamics is used. Defects of the lattice modify the dynamical matrix of the crystal which can be simply inverted in a case of a small defect density. The final formula describes the distribution of the scattered intensity of the incident light wave as a function of the defect configuration. The possibility of the extension of the method to the Laue theory is briefly discussed.     

Study of diffusion of wave packets in a square lattice under external fields along the discrete nonlinear Schrödinger equation

The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.     

3维U(1)改进格点规范理论中胶球质量和胶球波函数

用改进的格点规范场哈密顿量和截断本征方程法计算2+1维U(1)规范场的胶球质量(质量隙)和胶球波函数,结果显示出较好的标度行为.     

2+1维U(1)改进格点规范理论中0++胶球波函数的三阶结果

用改进的格点规范场哈密顿量和截断本征方程法计算2+1维U(1)规范场的0++胶球波函数，三阶结果比二阶结果的标度行为有了较大的改善.     

Fine structure of the diffraction image of an edge dislocation in high-resolution section topography

The propagation of an x-ray wave field in an elastic field of an edge dislocation crossing a scattering triangle exactly along the bisector of the scattering angle has been considered. The scattering of the x-ray wave field by a complex elastic field of the edge dislocation has been analyzed using the methods of geometrical optics. It has been established that the fine structure of a diffraction image of defects in thick crystals is determined by the differences in scattering of the normal and anomalous modes of the x-ray wave field in the vicinity of the Bragg reflection. In the case of thick crystals, the x-ray diffraction image of defects can have a symmetry different from the symmetry of the function of local misorientations of the crystal lattice. X-ray wave scattering by local distortions of the crystal lattice can occur according to two different mechanisms depending on the gradient of space changes in the deformation field. In the crystal regions where the elastic field varies slowly with a change in the distance, the x-ray wave field has had time to adjust itself to follow the course of deviations of the crystal lattice from the exact Bragg condition. In the crystal region where the elastic field changes significantly at distances of the order of the extinction length, this region leaves the reflecting position and interference scattering occurs at the interface of the region. It is important that the form of the deformation field in this case is of no significance.     

铈原子基态的理论研究

在有心力场近似和组态相互作用理论框架下,通过对电子波函数、各壳 层上电子的束缚能、半径、总束缚能的分析和计算,研究了Ce原子的可能的基组态及其基态 时的原子态。研究结果表明：基组态为4f5d,基态原子态为1G4。     

Quantum dynamics of charge transfer on the one-dimensional lattice:Wave packet spreading and recurrence

The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.     

Wave packets in graphene under external fields: Vortices formation

In this work we analyzed the time propagation of wave packets on a sheet of graphene under the action of external magnetic and electric fields in the Hall configuration. The treatment given in this work to the problem of particle propagation in graphene is based on the tight-binding model, not requiring to consider the linear approximation of the band structure around point K in the Brillouin zone. So, our calculation is able to describe the behavior of the particle in more general cases, not only the case of low lying excited states, the so-called massless Dirac electrons. Evaluating the time evolution of the wave function we assume as an initial state a Gaussian with a given velocity. We have considered the symmetric gauge for the vector potential. For specific cases one is able to show a very interesting effect such as the apparition of vortices, i.e., the initial wave is split into components each one of these forming vortices that remain stationaries as time goes. Moreover, for a packet with a wave vector near point K in the Brillouin zone, one is able to show the presence of the effect of zitterbewegung, that is, a trembling motion of the centroid of the wave packet. The inclusion of a dc electric field in the plane of the graphene lattice displaces the vortices in a direction perpendicular to the field.     

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.     

A phase cell approach to Yang-Mills theory

For the abelian Yang-Mills theory, a one-to-one correspondence is established between continuum gauge potentials and compatible lattice configurations on an infinite sequence of finer and finer lattices. The compatibility is given by a block spin transformation determining the configuration on a lattice in terms of the configuration on any finer lattice. Thus the configuration on any single lattice is not an approximation to the continuum field, but rather a subset of the variables describing the field.It is proven that the Wilson actions on the lattices monotonically increase to the continuum action as one passes to finer and finer lattices. Configurations that minimize the continuum action, subject to having the variables fixed on some lattice, are studied.This work was supported in part by the National Science Foundation under Grant No. PHY-85-02074     

On Some Solutions of Relativistic Wave Equations

In this paper we present exact solutions of the Klein-Gordon and the Dirac equations in different configurations of an electromagnetic field, which are characteristic for free-electron laser-type gauges. In the case of motion of a charge scalar particle in standing wave an energy spectrum is studied. For the motion of an electron in a so-called wiggler magnetic field a spinor wave function is proved to be obtainable. An undulator field configuration with propagating wave is treated also.     

2+1维U(1)格点规范场论中真空态的研究

对2+1维U(1)格点规范场论真空态进行研究,仔细推导出连续极限下真空谈函数中参数μ₀和μ₂的普适表达式,并用截断本征方程法进行数值计算.     

Lattice Wave of Magnetized Spherical Dust in Radio-Frequency Sheath with Negative Ions

Lattice wave of magnetized spherical dust in radio-frequency sheath with negative ions is investigated. The dispersion relation of two-dimensional hexagonal lattice horizontal wave and the influence of negative ions and magnetic field intensity on the wave are also investigated. The results show that for two-dimensional hexagonal horizontal lattice wave, negative ions reduce the wave frequency at the range of long-wavelength, whereas raising the wave frequency at the range of short-wavelength and magnetic field contributes to dropping the wave frequency a little.     

Topological aspects of gauge and spin potts models

For the d-dimensional lattice gauge Potts model the representation of the partition function is derived, where the field configuration summation is reduced to the summation over submanifolds (oriented and nonoriented), constructed from the plaquettes of the lattice. The topological invariants (Betti numbers) of these two-dimensional submanifolds are used in an essential way. Some possible applications of this representation for the partition function are discussed.     

Wave radiation in lattice fracture

The square and triangular lattices are considered, where the uniform crack growth is accompanied by the wave radiation. The radiation energy and structure are studied. The energy radiated to the bulk of the lattice is found in a direct way. The radiation structure is described based on the crack problem solution and by means of the analysis of two-dimensional dispersion relations for the intact lattice. The mode III problem for square lattice is discussed in detail, whereas, in the case of the plane problem for the triangular lattice, the only those results are derived which follow from the two-dimensional dispersion relations. It is shown that there exists a finite crack-speed-dependent region of wavenumbers corresponding to the waves radiated to the bulk of the lattice. In the case of the triangular-cell lattice, in addition, one or several lattice Rayleigh waves are radiated. For the square lattice a complete solution for the wave field is presented with the crack-speed-dependent far-field asymptote. The latter is characterized by the wave amplitude asymptotically decreasing as the distance from the crack front in power −1/3. The asymptotically significant crack-speed-dependent direction of the radiation is determined. Such asymptotic results are also valid for the triangular lattice.     

Landau levels and the Thomas-fermi structure of rapidly rotating bose-einstein condensates

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: (i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope function, which gives rise to components in higher Landau levels; (ii) the LLL wave function with a nonuniform vortex lattice. From variational calculations, we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice. The predicted distortions of the lattice are small, but in accord with recent measurements at lower rates of rotation.     

Charge Transfer in the Lattice with an Impurity Site. Reflection and Transmission of the Wave Packet

The quantum dynamics of the propagation of the charge wave function in a uniform lattice containing a single impurity site is considered. A nonstationary problem is solved in the tight-binding approximation. The initial state is the wave function fully localized at one of the lattice sites. The coefficients of transmission of the wave packet through the impurity site and reflections from it are calculated as a function of the parameters of the problem, that is, the additional energy on the impurity and the distance between the impurity and the initial position of the charge. The problem is solved for two types of boundary conditions: an infinite and a semi-infinite lattice. Good agreement with numerical simulation is obtained.     

Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice

The accessibility of the critical parameters for the superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice is investigated. We determine the hopping matrix element J, the on-site interaction U, and hence the ratio J/U, in the harmonic oscillator wave function approximation. We show that for a range of realistic parameters the critical values of J/U, predicted by different methods for the Bose-Hubbard model in 2D, such as mean field theory and Monte Carlo simulations, are accessible in a 2D permanent magnetic lattice. The calculations are performed for a 2D permanent magnetic lattice created by two crossed arrays of parallel rectangular magnets plus a bias magnetic field.