Decoupling by a projection

The asymptotic behaviour for μ→∞ of the family H+μP is investigated, where H is a semi-bounded but not bounded selfadjoint operator, P is an orthoprojection, H is local with respect to $\text{P}\text{?}\text{=1?P}$. A characterization of the Friedrichs extension of

by the strong resolvent convergence limit of the family H+μP (which exists) is given. Applications to differential operators and strengthening of the main result (as to convergence with respect to the trace norm for some power of the resolvent) are discussed. Also an application to certain two space scattering systems is given.     

Scattering of a dipole by a dipole

The spectrum of eigenvalues of the Schrödinger equation with a dipole-dipole potential is not bounded below. An appropriate cut-off leads to a correct low energy problem. Furthermore, it is shown that in polar coordinates the corresponding Schrödinger equation is separable for two spins 1/2.     

Focusing a charged-particle beam by a superconductor

We analyze the supertron experiments (the superconducting-cone focusing of electron beams). As the distinct features of superconductors from metals are concerned, the Meissner effect is considered as an alternative mechanism to explain the focusing function of the supertron. As a model study, we consider the system of a charged point particle moving in an infinite square cross-section hole through a superconductor. Using the method of images, we have studied the confined motion of the charged particle due to the self-induced magnetic field in the nonrelativistic regime. The relevant applications, in particular the focusing of electron and position beams, are discussed.     

A Diffusive System Driven by a Battery or by a Smoothly Varying Field

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit the long range pair correlation functions of the system driven by a battery are very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models.     

Scattering of a Bessel beam by a sphere

The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.     

Pairing by a Dynamical Interaction in a Metal

Journal of Experimental and Theoretical Physics - We consider pairing of itinerant fermions in a metal near a quantum-critical point (QCP) towards some form of particle-hole order (nematic,...     

Scattering of a plane wave by a nonlinear load array on a perfectly conducting shield covered by a dielectric layer

The problem of plane wave scattering by a nonlinear load array on a perfectly conducting shield covered by a homogeneous dielectric layer is solved by the integral equation method. The influence of the coating parameters on the array reflection coefficients at the fundamental and third harmonics of the incident wave are studied numerically. Taganrog Radiotechnical University, Taganrog, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 545–551, June, 2000.     

Numerical simulation of the two-phase flow produced by spraying a liquid by a nozzle

A numerical experiment on the simulation of the two-phase flow formed during spraying of a liquid by a nozzle has been described. The radial and axial velocity profiles of the droplets and gas in the free spray and in the two-phase flow through a cylindrical apparatus have been calculated and represented taking into account the early drag crisis of droplets and peculiarities of turbulent friction in the gas, which was detected in previous experiments. The distinguishing feature of the numerical model of the two-phase flow is that it employs the differential equations describing the nonstationary flow of a compressible gas as the initial equations. In transition to their difference analog, the familiar Lax–Wendorff algorithm has been used. A comparison of the results of calculations based on this model with experimental data has demonstrated their concordance.     

Generation of surface waves by a drag current generated by a focused femtosecond pulse

A new nonlinear optical phenomenon—generation of surface waves by a drag current appearing at an inclined incidence of a focused femtosecond laser pulse—has been theoretically described. The generated waves have terahertz frequencies and their total energy increases with an increase in the effective frequency of electron–electron collisions and with a decrease in their density.     

Self-imaging by a volume grating

The self-image phenomenon by a volume grating is proposed and theoretically analyzed. A theoretical model based on a path integral formulation to describe wave propagation through the grating inhomogeneous medium is applied. A modified version of the scalar diffraction theory Fresnel propagator is obtained which allows calculating the diffracted field amplitude by the grating. The proposed model is applied to amplitude and/or phase volume gratings. Remarkable features appear, in particular at the fractional Talbot distance 0.125z_T. In this case, if an in-phase real and imaginary grating modulation is considered a self-image intensity profile is observed for determined values of the absorptive and refractive parameters. On the other hand, a spatial comb intensity profile for a near half period shift between the real and imaginary grating modulations is found.     

X-ray scattering by a superlattice

X-ray scattering by a superlattice consisting of two types of alternating layers is considered, including both the statistical spread in the layer thicknesses and the phase slippage at inter-layer boundaries. The Bragg peak is not only smeared out, but it is also displaced by an amount proportional to the phase slippage.     

Nonadiabatic heating of a plasma produced by the ionization of a gas by a short intense laser pulse

A hydrodynamic model of the interaction of a short, intense laser pulse with moderate-density gases is constructed. The model systematically takes into account both tunneling-ionization processes and the relativistic motion of the electrons that are produced by the ionization of the gas in the relativistically strong field of the pulse. X-ray spectroscopy data agree well with the proposed theory. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 566–571 (10 October 1998)     

Plasma confinement by a picket-fence

A current produced line cusp field is shown to confine both plasma and primary ionizing electrons.     

Electrostatic potential screened by a two-dimensional electron system: a real-space observation by scanning-tunneling spectroscopy

Scanning-tunneling spectroscopy at 5 K was used to investigate the electrostatic potential profile on the Si(111)-square root of 3 x square root of 3 Ag surface at subnanometer spatial resolution. The potential was measured from an energy-level shift of electronic states on the surface. The potential images obtained reveal that the potential drops around the steps and Ag adsorbates, upon which positive charges are presumably accumulated. The profiles of the reduced potentials are explained with the screening of potential due to the charges by two-dimensional electron gas (2DEG) existing on the surface. The Friedel oscillation, which results from the screening and has a period of the half Fermi wavelength of the 2DEG, was also observed in the potential images.