Discrete Charges on a Two Dimensional Conductor

We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for “singular” domains. For smooth conductors, the locations of the charges can be determined, to within $O\left( {\sqrt {\log {N \mathord{\left/ {\vphantom {N {N^2 }}} \right. \kern-0em} {N^2 }}} } \right)$ by an integral equation due to Pommerenke [ Math. Ann., 179: 212–218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.     

The Nonsymmetric Kaluza–Klein Theory and Modern Physics A Novel Approach

We consider in the paper the Nonsymmetric Kaluza–Klein Theory finding a condition for a color confinement in the theory. We consider also a Kerner–Wong–Kopczyński equation in this theory. The Nonsymmetric Kaluza–Klein Theory with a spontaneous symmetry breaking and Higgs' mechanism is examined. We find a mass spectrum for a broken gauge bosons and Higgs' particles. We derive a generalization of Kerner–Wong–Kopczyński equation in the presence of Higgs' field. A new term in the equation is a generalization of a Lorentz force term for a Higgs' field. We consider also a bosonic part of GSW (Glashow–Salam–Weinberg) model in our theory, getting masses for W, Z bosons and for a Higgs' boson agreed with an experiment. We consider Kerner–Wong–Kopczyński equation in GSW model obtaining some additional charges coupled to Higgs' field.     

质心坐标系中分数量子Hall效应体系的能量本征值

本文在质心坐标系中讨论了分数量子Hall效应的少粒子体系。推导了一个适用于任意电子数的对体系电子角动量的可能组合加以限制的关系式。利用这一约束条件,体系哈密顿量的本征方程阶数大大削减,从而减少了数值计算的工作量。进一步,我们在质心坐标系中计算了当前计入正电背景影响用得较多的均匀正电背景模型和局域电中性模型的能量本征值作了数值计算。 关键词：     

Scanning tunneling spectroscopy of charge effects on semiconductor surfaces and atomic clusters

We have used scanning tunneling microscopy and scanning tunneling spectroscopy at liquid helium temperature to study the electronic structure of in situ cleaved, (110) oriented surfaces of InAs single crystals. Both unperturbed, atomically flat areas and areas with an atomic-size defect cluster have been investigated. We show that the anomalous behavior of the local tunneling conductivity, which indicates a pronounced enhancement of the semiconductor band gap for the flat areas, is consistent with band bending induced by charges localized at the apex of the tip. Atomic-size defect clusters contain additional charges which modify the band bending; this explains the different behavior of the tunneling conductivity near the defect cluster. The experimentally observed oscillations of the tunneling conductivity near the band gap edges can be directly related to resonant tunneling through quantized surface states which appear because of the band bending. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 130–135 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Geometrical optics in dispersive media

We present a systematic derivation of Geometrical Optics in dispersive media from Maxwell's equation for the presence of charges and currents, by using the two-timing approximation technique. A propagation equation for the polarisation plane is also derived.     

Asymptotic freedom in the Einstein-Cartan theory

The Einstein-Cartan theory with a cosmological constant and an external current is analyzed. Single-loop contraterms repeat the structure of the original action on the mass shell. This fact is utilized to write a renormalization-group equation for the effective charges associated with the cosmological constant and the square of the current. Asymptotic freedom is realized in the ultraviolet region for the new charges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 40–44, September, 1988.     

Accurate modelling of InGaN quantum wells

The internal field, the band structure and the oscillator strengths of the optical transitions of wurtzite strained InGaN quantum wells are accurately computed by a self-consistent solution of the Poisson equation and an eight-band k · p Schrödinger equation taking into account charges due to polarisation fields, doping and free carriers. The results are used to compare luminescence and gain spectra for single and triple quantum well structures and to elucidate the effect of the polarisation fields.     

Lowest Order Constrained Variational Calculation of Structure Properties of Protoneutron Star

We calculate the structure properties of protoneutron star such as equation of state, maximum mass, radius and temperature profile using the lowest order constrained variational method. We show that the mass and radius of protoneutron star decrease by decreasing both entropy and temperature. For the protoneutron star, it is shown that the temperature is nearly constant in the core and drops rapidly near the crust.     

Energy Mechanism of Charges Analyzed in Real Current Environment

We analyze in this work the energy transfer process of accelerated charges, the mass fluctuations accompanying this process, and their inertial properties. Based on a previous work, we use here the dipole antenna, which is a very convenient framework for such analysis, for analyzing those characteristics. We show that the radiation process can be viewed by two energy transfer processes: one from the energy source to the charges and the second from the charges into the surrounding space. Those processes, not being in phase, result in mass fluctuations. The same principle is true during absorption. We show that in a transient period between absorption and radiation the dipole antenna gains mass according to the amount of absorbed energy and loses this mass as radiated energy. We rigorously prove that the gain of mass, resulting from electrical interaction has inertial properties in the sense of Newton's third low. We arrive to this result by modeling the reacting spacetime region by an electric dipole.     

A microscopic semiclassical confining field equation forU(1) lattice gauge theory in 2+1 dimensions

We present a semiclassical nonlinear field equation for the confining field in 2+1-dimensionalU(1) lattice gauge theory (compact QED). The equation is derived directly from the underlying microscopic quantum Hamiltonian by means of truncation. Its nonlinearities express the dynamic creation of magnetic monopole currents leading to the confinement of the electric field between two static electric charges. We solve the equation numerically and show that it can be interpreted as a London relation in a dual superconductor.     

First-principles study on structural and electronic properties of AlNSix heterosheet

Under generalized gradient approximation (GGA), the structural and electronic properties of AlN and Si sheets, hydrogen terminated AlN and Si nanoribbons with hexagonal morphology and 2, 4, 6 zigzag chains across the ribbon width and the hexagonally bonded heterosheets AlNSi_x (x=2, 4, and 6) consisting of hexagonal networks of AlN (h-AlN) strips and silicene sheets with zigzag shaped borders have been investigated using the first-principles projector-augmented wave (PAW) formalism within the density function theory (DFT) framework. The AlN sheet is an indirect semiconductor with a band gap of 2.56 eV, while the Si sheet has a metallic character since the lowest unoccupied conduction band (LUCB) and the highest occupied valence band (HOVB) meet at one k point from Γ to Z. In the semiconductor 6-ZAlNNR, for example, the states of LUCB and HOVB at zone boundary Z are edge states whose charges are localized at edge Al and N atoms, respectively. In metallic 6-ZSiNR, a flat edge state is formed at the Fermi level E_F near the zone boundary Z because its charges are localized at edge Si atoms. The hybridizations between the edge states of h-AlN strips and silicene sheets result in the appearance of border states in the zigzag borders of heterosheets AlNSi_x whose charges are localized at two atoms of the borders with either bonding or antibonding π character.     

Gribov's equation for the Green function of light quarks

Gribov's scenario of supercritical charges in QCD is investigated. We perform a numerical study of the corresponding equation for the Green function of light quarks. This is done in an approximation which neglects all pion contributions. Different types of solutions in the Euclidean region are discussed and the mass function of the quark is calculated. The solutions of the equation are shown to have a qualitatively different behaviour if the strong coupling constant exceeds a critical value in the infrared region. Chiral symmetry breaking is found to occur at supercritical coupling. The analytic structure of the solutions is investigated. Earlier results obtained by Gribov are confirmed and extended. Received: 20 January 2000 / Published online: 6 March 2000     

Radiative transitions involving impurities

A many-electron development of effective-mass theory is given, based on a Hartree-Fock viewpoint. The procedure provides a basis for the calculation of polarization effects other than those produced by single point charges. An exact effective-mass differential equation is obtained, taking into account non-parabolicities of the band and gradients of the perturbation. Results are obtained for the matrix-element for dipole emission between two impurity-states in a semiconductor. When applied to the problem of donor-acceptor transfer, the results offer an explanation as to why the no-phonon process is considerably stronger in Ge than in Si, even though dielectric constant and effective-mass magnitude effects predict the opposite. The highly non-parabolic conduction band of Ge is responsible.     

Superradiance of Blackholes

The Klein-Gordon equation is separated and the superradiance phenomenon isstudied on five-parameter (mass, angular momentum, cosmological constant,electric and magnetic charges) black-hole spacetimes.     

Ultimate energy density of observable cold baryonic matter

We demonstrate that the largest measured mass of a neutron star establishes an upper bound to the energy density of observable cold baryonic matter. An equation of state-independent expression satisfied by both normal neutron stars and self-bound quark matter stars is derived for the largest energy density of matter inside stars as a function of their masses. The largest observed mass sets the lowest upper limit to the density. Implications from existing and future neutron star mass measurements are discussed.     

Stability of ferromagnetism in the Hubbard model on the kagome lattice

The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.     

Wave equation for vectons and magnetic charges

Based on the wave equation for spin-one particles (vectons) proposed earlier by the author, we select an interaction operator and then in the limit go to field variables and the Maxwell equations of classical electrodynamics. Additional terms arising in this case are interpreted as magnetic charges and currents. We discuss the consequences. We conclude that it is possible to find magnetic charges in matter and present some characteristics of such materials. We logically derive free magnetic charges and their currents. We construct an electrodynamics taking into account material media.Karachaevsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 49–54, September, 1994.     

黑洞的视界面公式

从零曲面方程出发,导出了黑洞视界面的普遍公式.利用高登方程验证了该公式的正确性,并利用该公式求出了任意加速含荷黑洞的视界. 关键词： 黑洞 视界 零曲面 乌龟坐标变换     

一维周期耗散媒质中的电磁波模及其数值分析

文中推导了一维周期耗散媒质中电磁波模式特征值方程,证明其解分类为一系列的"导带"和"禁带";用实数Re(K_z²)代替复特征值K_z标识模式,可清晰地显示出带结构,便于模式的分类和比较。文中用数值方法给出了几组参数下横电波、横磁波模最低两个带的图示,并与周期势场中的电子能带作了对比。     

Explicit mass renormalization and consistent derivation of radiative response of classical electron

The radiative response of the classical electron is commonly described by the Lorentz–Abraham–Dirac (LAD) equation. Dirac’s derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: “We... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwanted terms”. To substantiate Dirac’s approach and clarify the mass renormalization, we introduce the point charge as a limit of extended charges contracting to a point; the fulfillment of conservation laws follows from the relativistic covariant Lagrangian formulation of the problem. We derive the relativistic point charge dynamics described by the LAD equation from the extended charge dynamics in a localization limit by a method which can be viewed as a refinement of Dirac’s approach in the spirit of Ehrenfest theorem. The model exhibits the mass renormalization as the cancellation of Coulomb energy with the Poincaré cohesive energy. The value of the renormalized mass is not postulated as an arbitrary constant, but is explicitly calculated. The analysis demonstrates that the local energy–momentum conservation laws yield dynamics of a point charge which involves three constants: mass, charge and radiative response coefficient θ$\theta$. The value of θ$\theta$ depends on the composition of the adjacent potential which generates Poincaré forces. The classical value of the radiative response coefficient is singled out by the global requirement that the adjacent potential does not affect the radiated energy balance and affects only the local energy balance involved in the renormalization.