4,957 research outputs found
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 are investigated. We impose the Neumann
boundary condition on the two concentric windows of the radii and
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 .
When and 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 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 , 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 direction of the (24) 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
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