Steplike currents in confined two dimensional systems

In a confined two dimensional system of non-interacting electrons in a normal constant magnetic field, the current is calculated along the sample as a response to an electric field in the same direction which is switched on and then off. The resulting stationary current is shown to be a step-like function of the electron density.     

Solution of two mutually-reducible problems in electrostatics

There are two well-known problems in electrostatics whose solutions reduce to each other. One of them is that of a grounded conductor containing a cavity with given boundary . A charge distribution is specified on another surface S inside the cavity, or within the volume enclosed by S. It is required to find the charge density induced on . The other problem is that of finding “equivalent” sets of charges (producing identical external fields). Here again there are surfaces and S and the same original distributed charge as in the first problem, but the system is now in empty space and the problem is to find the charge distribution on that produces the same external field as the given distribution on S. Mutual reducibility means that it is sufficient to consider one of the two problems, say, the second. The problem examined in this paper is that of confocal ellipsoids S and and charge distributions described in terms polynomial functions of Cartesian coordinates. The method of multipole moments which leads directly to the solution (i.e., without the need to evaluate the field) is described. Analytical solutions are given for simple surface and volume charge distributions. Special and limiting cases are examined, including degenerate surfaces S and in the form of confocal elliptic cylinders. Zh. Tekh. Fiz. 67, 1–6 (April 1997)     

The quasi-exactly solvable problems for two dimensional quantum systems

In this paper, we study the quasi-exactly solvable problems for two dimensional quantum systems. By using the Bethe ansatz method, we obtain the general form of the quasi-exactly solvable potential. Then, we present several examples to give the specific forms of quasi-exactly solvable potentials. In the examples, some physical models of quasi-exactly solvable problems are re-exhibited.     

Strong-coupling electrostatics for two dissimilar charged walls

We study the effective interaction between two parallel charged plates, modelling macromolecules, or colloids, in the strongly coupled Coulomb regime. Neutralizing mobile ions are point-like and confined in the inter-plate slab. A cumulant technique provides exact expansions, beyond the leading strong-coupling order, that are in remarkable agreement with simulation data for both the ionic profile and the inter-plate pressure. The present approach amounts to a summation over relevant excitations around the Wigner Crystal ground state formed at infinite coupling; It thereby differs from previous virial-like strong-coupling theories and generalizes a recent work by the authors to asymmetric plates.     

Dynamical method for studying localization-delocalization transition in two dimensional percolating systems

We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is determined by the disorder and interference effects, leading to interesting sharp features in conductance as the energy, disorder, and boundary conditions are varied. To aid understanding of this phenomenon, we develop a visualization method whereby the progression of a wave packet entering the cluster through a lead on one side and exiting from another lead on the other side can be tracked dynamically. Using this method, we investigate the localization-delocalization transition in a 2D system for various boundary conditions. Our results indicate the existence of two different kinds of localized regimes, namely exponential and power law localization, depending on the amount of disorder. Our study further suggests that there may be a delocalized state in the 2D quantum percolation system at very low disorder. These results are based on a finite size scaling analysis of the systems of size up to 70 × 70 (containing 4900 sites) on the square lattice.     

On the symmetry of the Gibbs states in two dimensional lattice systems

Under fairly general conditions if a two dimensional classical lattice system has an internal symmetry groupG, which is a compact connected Lie group, then all Gibbs states areG-invariant.     

Four dimensional realization of two dimensional current groups

The quotient realization of the central extensions of the current groups over Riemann surfaces is achieved by means of the Leray residue theory. This approach replaces de Rham cohomology in the classical WZNW construction for affine Lie groups.     

Global weak solutions and attractors of the three dimensional Maxwell-Bloch two level laser systems

The three-dimensional Maxwell-Bloch system governs the multi-longitudinal and transverse mode dynamics of two level wide aperture lasers in an optical ring cavity. The system is hyperbolic in the propagation direction, and dispersive in the transverse directions due to diffraction effects. A rich variety of optical patterns and chaos are present in the dynamics. We show the global existence of weak solutions inL ^p (2p<) spaces of the Maxwell-Bloch system under both absorbing and periodic boundary conditions. The weak solutions are unique within the class of solutions provided by our regularization procedure and approach a universal attractor which has only partial smoothing instead of theC smoothing property found in early works for the (longitudinal) one-dimensional and (transverse) two-dimensional cases. The idea of the proof makes essential use of both the hyperbolicity and dispersivity of the system. In the case of periodic boundary condition, our result depends on a conjectural Strichartz inequality.     

电场线两大性质是静电场两大定理的形象表述

谁都知道电场线起于正电荷,止于负电荷,在无电荷处不中断.我们称此为电场线的性质1.你知道这是高斯定理的逻辑结果吗?你知道"没有高斯定理就没有性质1吗"?可是有人喜欢用"电场线在无电荷处不中断"这一性质轻易地证明高斯定理,这就犯了因果倒置的逻辑错误.     

Melting in a two dimensional system with dipole interaction

Molecular-dynamics simulations show that the solid-liquid phase transition in a two-dimensional system of dipoles is of first order. The translational and orientational correlation function, the static form-factor and the dielectric function are calculated. We analyze also the self-diffusion coefficient. It is seen that self-diffusion takes place mainly on the cluster boundaries.     

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.     

Statistical mechanics of two dimensional tilings

Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4.     

Small divisors with spatial structure in infinite dimensional Hamiltonian systems

A general perturbation theory of the Kolmogorov-Arnold-Moser type is described concerning the existence of infinite dimensional invariant tori in nearly integrable hamiltonian systems. The key idea is to consider hamiltonians with aspatial structure and to express all quantitative aspects of the theory in terms of rather general weight functions on such structures. This approach combines great flexibility with an effective control of the vrious interactions in infinite dimensional systems.Supported by Sonderforschungsbereich 256 at the University of Bonn     

Transport in two dimensional electronic micro-emulsions

In two dimensional electron systems with Coulomb or dipolar interactions, a direct transition, whether first or second order, from a liquid to a crystalline state is forbidden. As a result, between these phases there must be other (micro-emulsion) phases which can be viewed as a meso-scale mixture of the liquid and crystalline phases. We investigate the transport properties of these new electronic phases and present arguments that they are responsible for the various transport anomalies that have been seen in experiments on the strongly correlated 2DEG in high mobility semiconductor devices with low electron densities.     

Spontaneous breakdown in two dimensional space-time

We prove that in two-dimensional space-time, symmetry transformations which are generated by Poincaré covariant currents can not be spontaneously broken. This is also the case with the dilation current. We argue that other currents which involve explicit space-time dependence might lead to spontaneously broken symmetries accompanied by massless Goldstone bosons. We construct a trivial example where this phenomenon occurs.     

激光二维光机扫描系统设计

介绍了一种采用八面体转镜与平面摆镜联合实现激光二维光栅轨迹扫描的扫描器，讨论了光学及机构设计中影响扫描精度的因素，及电机频率／相位稳速控制问题，保证了该扫描器的精度和稳定性。