7,873 research outputs found
Positivity of Lyapunov exponents for a continuous matrix-valued Anderson model
We study a continuous matrix-valued Anderson-type model. Both leading
Lyapunov exponents of this model are proved to be positive and distinct for all
ernergies in except those in a discrete set, which leads to
absence of absolutely continuous spectrum in . This result is an
improvement of a previous result with Stolz. The methods, based upon a result
by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a
criterion by Goldsheid and Margulis, allow for singular Bernoulli
distributions
The inverse electromagnetic scattering problem in a piecewise homogeneous medium
This paper is concerned with the problem of scattering of time-harmonic
electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous
medium. The well-posedness of the direct problem is established, employing the
integral equation method. Inspired by a novel idea developed by Hahner [11], we
prove that the penetrable interface between layers can be uniquely determined
from a knowledge of the electric far field pattern for incident plane waves.
Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity
relation is obtained and used to show that the impenetrable obstacle with its
physical property can also be recovered. Note that the wave numbers in the
corresponding medium may be different and therefore this work can be considered
as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio
In-orbit Vignetting Calibrations of XMM-Newton Telescopes
We describe measurements of the mirror vignetting in the XMM-Newton
Observatory made in-orbit, using observations of SNR G21.5-09 and SNR
3C58 with the EPIC imaging cameras. The instrument features that complicate
these measurements are briefly described. We show the spatial and energy
dependences of measured vignetting, outlining assumptions made in deriving the
eventual agreement between simulation and measurement. Alternate methods to
confirm these are described, including an assessment of source elongation with
off-axis angle, the surface brightness distribution of the diffuse X-ray
background, and the consistency of Coma cluster emission at different position
angles. A synthesis of these measurements leads to a change in the XMM
calibration data base, for the optical axis of two of the three telescopes, by
in excess of 1 arcminute. This has a small but measureable effect on the
assumed spectral responses of the cameras for on-axis targets.Comment: Accepted by Experimental Astronomy. 26 pages, 18 figure
Inverse Scattering for Gratings and Wave Guides
We consider the problem of unique identification of dielectric coefficients
for gratings and sound speeds for wave guides from scattering data. We prove
that the "propagating modes" given for all frequencies uniquely determine these
coefficients. The gratings may contain conductors as well as dielectrics and
the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page
Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements
International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases
Physics Analysis Expert PAX: First Applications
PAX (Physics Analysis Expert) is a novel, C++ based toolkit designed to
assist teams in particle physics data analysis issues. The core of PAX are
event interpretation containers, holding relevant information about and
possible interpretations of a physics event. Providing this new level of
abstraction beyond the results of the detector reconstruction programs, PAX
facilitates the buildup and use of modern analysis factories. Class structure
and user command syntax of PAX are set up to support expert teams as well as
newcomers in preparing for the challenges expected to arise in the data
analysis at future hadron colliders.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics
(CHEP03), La Jolla, Ca, USA, March 2003, 7 pages, LaTeX, 10 eps figures. PSN
THLT00
Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension
In this article we prove an upper bound for the Lyapunov exponent
and a two-sided bound for the integrated density of states at an
arbitrary energy of random Schr\"odinger operators in one dimension.
These Schr\"odinger operators are given by potentials of identical shape
centered at every lattice site but with non-overlapping supports and with
randomly varying coupling constants. Both types of bounds only involve
scattering data for the single-site potential. They show in particular that
both and decay at infinity at least like
. As an example we consider the random Kronig-Penney model.Comment: 9 page
Low lying spectrum of weak-disorder quantum waveguides
We study the low-lying spectrum of the Dirichlet Laplace operator on a
randomly wiggled strip. More precisely, our results are formulated in terms of
the eigenvalues of finite segment approximations of the infinite waveguide.
Under appropriate weak-disorder assumptions we obtain deterministic and
probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas
argument allows us to obtain so-called 'initial length scale decay estimates'
at they are used in the proof of spectral localization using the multiscale
analysis.Comment: Accepted for publication in Journal of Statistical Physics
http://www.springerlink.com/content/0022-471
A matrix-valued point interactions model
We study a matrix-valued Schr\"odinger operator with random point
interactions. We prove the absence of absolutely continuous spectrum for this
operator by proving that away from a discrete set its Lyapunov exponents do not
vanish. For this we use a criterion by Gol'dsheid and Margulis and we prove the
Zariski denseness, in the symplectic group, of the group generated by the
transfer matrices. Then we prove estimates on the transfer matrices which lead
to the H\"older continuity of the Lyapunov exponents. After proving the
existence of the integrated density of states of the operator, we also prove
its H\"older continuity by proving a Thouless formula which links the
integrated density of states to the sum of the positive Lyapunov exponents
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