Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $b$ located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any $a,b>0$. When $a$ and $b$ tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure

Propagation of axions in a strongly magnetized medium

The polarization operator of an axion in a degenerate gas of electrons occupying the ground-state Landau level in a superstrong magnetic field $H\gg H_0=m_e^2c^3/e\hbar =4.41\cdot 10^{13}$ G is investigated in a model with a tree-level axion-electron coupling. It is shown that a dynamic axion mass, which can fall within the allowed range of values $(10^{-5} eV \lesssim m_a\lesssim 10^{-2} eV)$, is generated under the conditions of strongly magnetized neutron stars. As a result, the dispersion relation for axions is appreciably different from that in a vacuum.Comment: RevTex, no figures, 13 pages, Revised version of the paper published in J. Exp. Theor. Phys. {\bf 88}, 1 (1999

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

Use of accelerated helium-3 ions for determining oxygen and carbon impurities in some pure materials

Methods are developed for the determination of O impurity in Be and Si carbide and concurrent determination of C and O impurities in Si and W by irradiation with accelerated He-3 ions and subsequent activity measurements of C-11 and F-18 formed from C and O with the aid of a gamma-gamma coincidence spectrometer. Techniques for determining O in Ge and Ga arsenide with radiochemical separation of F-18 are also described

Fast atom diffraction inside a molecular beam epitaxy chamber, a rich combination

Two aspects of the contribution of grazing incidence fast atom diffraction (GIFAD) to molecular beam epitaxy (MBE) are reviewed here: the ability of GIFAD to provide \emph{in-situ} a precise description of the atomic-scale surface topology, and its ability to follow larger-scale changes in surface roughness during layer-by-layer growth. Recent experimental and theoretical results obtained for the He atom beam incident along the highly corrugated $[ 1\bar{1}0 ]$ direction of the $\beta_{2}$(2$\times$4) reconstructed GaAs(001) surface are summarized and complemented by the measurements and calculations for the beam incidence along the weakly corrugated [010] direction where a periodicity twice smaller as expected is observed. The combination of the experiment, quantum scattering matrix calculations, and semiclassical analysis allows in this case to reveal structural characteristics of the surface. For the in situ measurements of GIFAD during molecular beam epitaxy of GaAs on GaAs surface we analyse the change in elastic and inelastic contributions in the scattered beam, and the variation of the diffraction pattern in polar angle scattering. This analysis outlines the robustness, the simplicity and the richness of the GIFAD as a technique to monitor the layer-by-layer epitaxial growth

Optimization of a Langmuir-Taylor detector for lithium

This paper describes the construction and optimization of a Langmuir-Taylor detector for lithium, using a rhenium ribbon. The absolute detection probability of this very sensitive detector is measured and the dependence of this probability with oxygen pressure and surface temperature is studied. Sources of background signal and their minimization are also discussed in details. And a comparison between our data concerning the response time of the detector and literature values is given. A theoretical analysis has been made: this analysis supports the validity of the Saha-Langmuir law to relate the ionization probability to the work function. Finally, the rapid variations of the work function with oxygen pressure and temperature are explained by a chemical equilibrium model.Comment: 11 pages, 7 figures, to appear in Rev. Sci. Instru

Dynamic screening of a localized hole during photoemission from a metal cluster

Recent advances in attosecond spectroscopy techniques have fueled the interest in the theoretical description of electronic processes taking place in the subfemtosecond time scale. Here we study the coupled dynamic screening of a localized hole and a photoelectron emitted from a metal cluster using a semi-classical model. Electron density dynamics in the cluster is calculated with Time-Dependent Density Functional Theory and the motion of the photoemitted electron is described classically. We show that the dynamic screening of the hole by the cluster electrons affects the motion of the photoemitted electron. At the very beginning of its trajectory, the photoemitted electron interacts with the cluster electrons that pile up to screen the hole. Within our model, this gives rise to a significant reduction of the energy lost by the photoelectron. Thus, this is a velocity dependent effect that should be accounted for when calculating the average losses suffered by photoemitted electrons in metals.Comment: 15 pages, 5 figure