A Simple Bimodular Nonlinear Element

We have studied the dynamics of an artificial nonlinear element representing a flexible membrane with oscillation limiters and a static pressing force. Such an element has the property of “bimodularity” and demonstrates “modular” nonlinearity. We have constructed a mathematical model that describes these oscillations. Their shapes have been calculated. We follow the analogy with a classical object—Galileo’s pendulum. We demonstrate that for a low-frequency excitation of the membrane, the level of the harmonics in the spectrum is higher than in the vicinity of the resonance frequency. We have established a strong dependence of the level of the harmonics on the magnitude of the pressing force for a weak perturbation. We propose a design scheme for a device in the quasi-static approximation possessing the property of bimodularity. We perform an experiment that confirms its operability. We show a qualitative coincidence of the experimental results and calculations when detecting an amplitude-modulated signal.     

Resistive Plates Carrying a Steady Current: Electric Potential and Surface Charges Close to the Battery

We treat the problem of two resistive plates carrying a steady current in the same direction. We consider a linear battery orthogonal to the direction of the current in the middle of the plates. We study the behavior of the surface charges close to the battery. We calculate the potential and electric field in the space outside the plates. We also consider the case of a single resistive plate carrying a steady current.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.     

Conformally Flat Spacetimes and Weyl Frames

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker’s interpretation of Nordstr?m scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame.     

Double-Pulse Spectra and Closed-Orbits: Photodetachment of H-in Parallel Electric and Magnetic Fields

We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulsephotodetachment spectra of H- in the presence of parallel electric and magnetic fields. We analyze the spectra in termsof closed-orbits of the system. We suggest a method for the measurement of a phase associated with each closed-orbit.     

Consistent treatment of charm evolution in deep inelastic scattering

We present a formulation which allows heavy quark mass effects to be explicitly incorporated in both the coefficient functions and the splitting functions in the parton evolution equations. We obtain a consistent procedure for evolution through the threshold regions for and production in deep inelastic scattering, which allows the prediction of the charm and bottom quark densities. We use the new formulation to perform a next-to-leading order global parton analysis of deep inelastic and related hard scattering data. We find that the optimum fit has . We give predictions for the charm components of the proton structure functions and as functions of and and, in particular, find that is in good agreement with the existing measurements. We examine the range of validity of the photon-gluon fusion model for electroproduction. We emphasize the value of a precision measurement of the charm component at HERA. Received: 12 May 1997 / Revised version: 12 June 1997     

Universality of entropy scaling in one dimensional gapless models

We consider critical models in one dimension. We study the ground state in the thermodynamic limit (infinite lattice). We are interested in an entropy of a subsystem. We calculate the entropy of a part of the ground state from a space interval (0,x). At zero temperature it describes the entanglement of the part of the ground state from this interval with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at any temperature. At zero temperature our formula reproduces a logarithmic formula, discovered by Vidal, Latorre, Rico, and Kitaev for spin chains. We prove our formula by means of conformal field theory and the second law of thermodynamics. Our formula is universal. We illustrate it for a Bose gas with a delta interaction and for the Hubbard model.     

Josephson pancakes in layered superconductors

We consider a pancake vortex in a layered superconductor with linear defects in the superconducting planes. We treat these defects as Josephson junctions. We show that the tunneling Josephson current through these junctions results in a pancake with a superconducting core. We find the mobility of a Josephson pancake.     

Radiation due to Josephson oscillations in layered superconductors

We derive the power of direct radiation into free space induced by Josephson oscillations in intrinsic Josephson junctions of layered superconductors. We consider the superradiation regime for a crystal cut in the form of a thin slice parallel to the c axis. We find that the radiation correction to the current-voltage characteristic in this regime depends only on crystal shape. We show that at a large number of junctions oscillations are synchronized providing high radiation power and efficiency in the terahertz frequency range. We discuss the crystal parameters and bias current optimal for radiation power and crystal cooling.     

Tail wavelets in merger of binary compact objects

We present a model for tail wavelets, a phenomenon known as "echo" in the literature. The tail wavelet may appear in signal reconnaissances in the merger of binary compact objects, including black holes and neutron stars. We show that the dark matter surrounding the compact objects lead to a speculated tail wavelet following the main gravitational wave(GW). We demonstrate that the radiation pressure of the main wave is fully capable of pushing away the surrounding matter to some altitude, and splashing down of the matter excites the tail wavelet after ringing down of the main wave. We illustrate this concept in a simplified model, where numerical estimations are conducted on the specific distribution of dark matter outside the black hole horizon and the threshold values in accordance with observations. We study the full back reaction of the surrounding dark matter to the metric and find that the effect on to the tail wavelets is insignificant. We reveal the fine difference between the tail wavelets of a dressed and a bare black hole. We demonstrate that the tail wavelet can appear as a natural phenomenon in the frame of general relativity, without invoking modified gravities or quantum effects.     

Absorption spectrum around nu=1: evidence for a small-size Skyrmion

We measure the absorption spectrum of a two-dimensional electron system (2DES) in a GaAs quantum well in the presence of a perpendicular magnetic field. We focus on the absorption spectrum into the lowest Landau level around nu=1. We find that the spectrum consists of bound electron-hole complexes, trionlike and excitonlike. We show that their oscillator strength is a powerful probe of the 2DES spatial correlations. We find that near nu=1 the 2DES ground state consists of Skyrmions of small size (a few magnetic lengths).     

Effective dielectric constant of dilute polydisperse suspensions of spheres

We study the effective dielectric constant of a dilute, polydisperse suspension of spheres embedded in a uniform background. We consider a frequency region where the dipole polarizability of individual spheres exhibits a resonance. We evaluate the effective dielectric constant to second order in the volume fraction employing the dipole approximation, which in previous work has been shown to be applicable in resonance. We apply our results to suspensions of spheres with identical and uniform dielectric constant, assuming a log-normal distribution of sphere radii.     

Simulations of the Hubbard model

We discuss results of simulations of the Hubbard model of interacting electrons on a lattice. We start with a brief discussion of methodology and point out some of the outstanding problems. We then discuss results of simulations of the model in three, two, and one dimension, particularly in connection with its magnetic and superconducting properties. We conclude with a brief discussion of future directions.     

Nonlinear localized modes in Glauber-Fock photonic lattices

We study a nonlinear Glauber-Fock lattice and the conditions for the excitation of localized structures. We investigate the particular linear properties of these lattices, including linear localized modes. We investigate numerically nonlinear modes centered in each site of the lattice. We found a strong disagreement of the general tendency between the stationary and the dynamical excitation thresholds. We define a new parameter that takes into account the stationary and dynamical properties of localized excitations.     

High-energy neutron spectrometry

We review progress made in the last quarter of a century in the field of neutron spectrometry over a wide energy range from ??1 MeV to a few tens of GeV. We consider spectrometers and detectors constructed in various laboratories for neutron measurements in numerous fundamental and applied studies. We discuss the results of works devoted to the development of experimental methods and the elaboration of new detectors. We pursue some promising avenues of further investigations.     

Relativistic quantum field theory with fractional spin and statistics

We construct a relativistic quantum field theory in 2 + 1 dimensions whose Fock states provide a multivalued representation of the Poincaré group. We add a topological term to the action of a scalar field theory and we show that this endows the path integral of the theory with an operator-valued cocycle which modifies the transformation properties of physical states. We demonstrate that one-particle states carry (in general) fractional spin. We determine the spin of many-particle states and we prove a generalized spin-statistics relation. We propose an equation of motion for on-shell states which generalizes naturally the Dirac equation.     

Investigation of spontaneously generated coherence in dressed states of (85)Rb atoms

We investigate the effects of spontaneously generated coherence (SGC) on the electromagnetically induced transparency features in a four-level Lambda-type system. We show that double-transparency windows and a controllable narrow absorption peak can be obtained with the presence of SGC. We present an equivalent system without the rigorous requirement of close-lying levels to observe the phenomena. We also experimentally demonstrate the corresponding features in a rubidium atomic beam.     

Quantum quench in the transverse-field Ising chain

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.