Topological states at exceptional points

We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of topologically distinct systems. We discuss that topological states appear even in closed systems. We explore dynamical robustness of exceptional edge states.     

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.     

Diffusion controlled multiplicative process: typical versus average behaviour

We investigate the dynamics of the number of particles diffusing in a multiplicative medium. We show that the typical behaviour of the growth process is different from the average. We develop a new formalism to study the average growth process and extend it to the calculation of higher moments and finally of the probability distribution. We show that the fluctuations of the growth process increase exponentially with time. We describe the interesting features of the distribution.     

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.     

Oblique propagation of longitudinal waves in magnetized spin-1/2 plasmas: Independent evolution of spin-up and spin-down electrons

We consider quantum plasmas of electrons and motionless ions. We describe separate evolution of spin-up and spin-down electrons. We present corresponding set of quantum hydrodynamic equations. We assume that plasmas are placed in an uniform external magnetic field. We account different occupation of spin-up and spin-down quantum states in equilibrium degenerate plasmas. This effect is included via equations of state for pressure of each species of electrons. We study oblique propagation of longitudinal waves. We show that instead of two well-known waves (the Langmuir wave and the Trivelpiece–Gould wave), plasmas reveal four wave solutions. New solutions exist due to both the separate consideration of spin-up and spin-down electrons and different occupation of spin-up and spin-down quantum states in equilibrium state of degenerate plasmas.     

Density,phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential

We present a detailed numerical study of the dynamics of a disordered one-dimensional Bose-Einstein condensates in position and momentum space. We particularly focus on the region where non-linearity and disorder simultaneously effect the time propagation of the condensate as well as the possible interference between various parts of the matter wave. We report oscillation between spatially extended and localized behavior for the propagating condensate which dies down with increasing non-linearity. We also report intriguing behavior of the phase fluctuation and the coherence properties of the matter wave. We also briefly compare these behavior with that of a two-dimensional condensate. We mention the relevance of our results to the related experiments on Anderson localization and indicate the possibility of future experiments     

Some properties of biwave maps

We study biwave maps and equivariant biwave maps. We obtain the formulations for equivariant biwave maps into various spaces by applying eigenmaps between spheres. We compute the biwave fields of inclusions into warped product manifolds and construct examples of biwave maps. We finally investigate the stress bi-energy tensors and the conservation laws of biwave maps.     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

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     

Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.     

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.     

Resonant X-ray diffraction: Basic theoretical principles

We present the main steps governing the theory of resonant X-ray diffraction (RXD). We focus on the derivation of the anomalous scattering amplitude from perturbation theory and starting from the low-energy expansion of the Dirac Hamiltonian. We give the main ingredients of the multipolar expansion in term of electric and magnetic transitions. We also show the expansion in terms of scattering tensors of the material. We end by giving the RXD formula necessary to simulate in practice this spectroscopy.     

Growth and Characterization of Pure and Thiourea-Doped L-Alanine Single Crystals for NLO Devices

We successfully grow single crystals of pure and thiourea-doped glycyl-L-alanine hydrochloride (GLAH and TU-GLAH) from aqueous solutions by the slow evaporation technique. We study the effect of thiourea dopant on the crystal properties. Single-crystal X-ray techniques confirm the crystal structure and change in the lattice-parameter values for the doped crystals. We analyze the doped crystals quantitatively by energy-dispersive X-ray analysis (EDAX) and confirm the presence of thiourea in the pure samples. We obtain the second-harmonic generations for the grown crystals using a Nd:YAG laser. We determine values of the work hardening coefficient from the microhardness study. We measure the values of the dielectric constant and dielectric losses in order to understand the electrical phenomena taking place in pure and TU-GLAH crystals.     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Apertureless near-field laser nanotechnology

We consider apertureless near-field optics that provides subwavelength resolution. We study the enhancement of the electromagnetic field near nanospheres and under the tip of a scanning probe microscope using the finite difference time-domain (FDTD) method. We discuss the mechanisms of field enhancement connected with the system geometry (“lightning rod effect”) and resonance excitation of local plasmon eigenmodes for different materials of the tip and various geometrical parameters of the system. We describe the possible applications in nano-optics and nanotechnology. We present the experimental achievements in apertureless near-field nanolithography.     

Multiplexing encryption technique by combining random amplitude and phase masks

We propose and demonstrate an encryption-selectable undercover multiplexing. We encrypt and multiplex images for storage by means of a random phase mask common to every image, covered with random amplitude masks different for each image. In order to get a correct decryption of the encoded information, we have to use the appropriate random amplitude mask; otherwise fake information is recovered. We employ a phase conjugation scheme to generate the recovering wavefronts. We analyze and compare the different alternatives and degrees of complexity this combination of masks brings to enhance the security of optical encrypting techniques. We also include an analysis on the advantages and disadvantages this undercover multiplexing protocol offers. We present digital simulations to demonstrate the soundness of the proposal.     

Optical manipulation of microparticles using whispering-gallery modes in a silicon nitride microdisk resonator

We demonstrate optical manipulation of 1?μm sized polystyrene microparticles on silicon nitride microdisk resonator devices using whispering-gallery modes in an integrated optofluidic chip. We demonstrate multiple trapping tracks and extended trapping ranges within single wavelengths through exciting high-order modes. We observe various sets of trapping tracks and ranges through exciting various resonance modes. We switch particle traveling tracks by tuning the laser wavelength to various wavelengths. We also observe microparticles assembling along the trapping tracks.     

Heavy-baryon properties with NLO accuracy in perturbative QCD

We present an analysis of the static properties of heavy baryons at next-to-leading order in the perturbative expansion of QCD. We obtain analytical next-to-leading order three-loop results for the two-point correlators of baryonic currents with one finite-mass quark field for a variety of quantum numbers of the baryonic currents. We consider both the massless limit and the HQET limit of the correlator as special cases of the general finite-mass formula and find agreement with previous results. We present closed-form expressions for the moments of the spectral density. We determine the residues of physical baryon states using sum-rule techniques.