1,016 research outputs found
Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains
We establish a limiting absorption principle for Dirichlet Laplacians in
quasi-cylindrical domains. Outside a bounded set these domains can be
transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet
Laplacians model quantum or acoustically-soft waveguides associated with
quasi-cylindrical domains. We construct a uniquely solvable problem with
perfectly matched layers of finite length. We prove that solutions of the
latter problem approximate outgoing or incoming solutions with an error that
exponentially tends to zero as the length of layers tends to infinity. Outgoing
and incoming solutions are characterized by means of the limiting absorption
principle.Comment: to appear in SIAM Journal on Mathematical Analysi
Relation between the Ultrasonic Attenuation and the Porosity of a RTM Composite Plate
AbstractWe propose a comparative study of X-ray tomography and ultrasonic reflection methods, for determining the porosity of a composite plate realized in LOMC with an industrial process. We measure the attenuation of ultrasound propagating in the thickness by using 10MHz plane transducer in pulse-echo mode. Comparing these results to the 2D porosity tomographic map allows establishing a relation between attenuation and porosity. A C-scan picture of the plate given by the echoes reflected by the rear surface also provides a local information on the attenuation. Furthermore, we propose a method for the mapping of the reflecting sources as the included bubbles and the interfaces resin/fibers
Energy Conservation Constraints on Multiplicity Correlations in QCD Jets
We compute analytically the effects of energy conservation on the
self-similar structure of parton correlations in QCD jets. The calculations are
performed both in the constant and running coupling cases. It is shown that the
corrections are phenomenologically sizeable. On a theoretical ground, energy
conservation constraints preserve the scaling properties of correlations in QCD
jets beyond the leading log approximation.Comment: 11 pages, latex, 5 figures, .tar.gz version avaliable on
ftp://www.inln.unice.fr
Topological code Autotune
Many quantum systems are being investigated in the hope of building a
large-scale quantum computer. All of these systems suffer from decoherence,
resulting in errors during the execution of quantum gates. Quantum error
correction enables reliable quantum computation given unreliable hardware.
Unoptimized topological quantum error correction (TQEC), while still effective,
performs very suboptimally, especially at low error rates. Hand optimizing the
classical processing associated with a TQEC scheme for a specific system to
achieve better error tolerance can be extremely laborious. We describe a tool
Autotune capable of performing this optimization automatically, and give two
highly distinct examples of its use and extreme outperformance of unoptimized
TQEC. Autotune is designed to facilitate the precise study of real hardware
running TQEC with every quantum gate having a realistic, physics-based error
model.Comment: 13 pages, 17 figures, version accepted for publicatio
Emergence of a confined state in a weakly bent wire
In this paper we use a simple straightforward technique to investigate the
emergence of a bound state in a weakly bent wire. We show that the bend behaves
like an infinitely shallow potential well, and in the limit of small bending
angle and low energy the bend can be presented by a simple 1D delta function
potential.Comment: 4 pages, 3 Postscript figures (uses Revtex); added references and
rewritte
Generalised Factorial Moments and QCD Jets
{ In this paper we present a natural and comprehensive generalisation of the
standard factorial moments (\clFq) analysis of a multiplicity distribution.
The Generalised Factorial Moments are defined for all in the complex plane
and, as far as the negative part of its spectrum is concerned, could be useful
for the study of infrared structure of the Strong Interactions Theory of high
energy interactions (LEP multiplicity distribution under the ). The
QCD calculation of the Generalised Factorial Moments for negative is
performed in the double leading log accuracy and is compared to OPAL
experimental data. The role played by the infrared cut-off of the model is
discussed and illustrated with a Monte Carlo calculation. }Comment: 11pages 4 figures uuencode, LATEC, INLN 94/
On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum
of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha,
with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay
as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously
differentiable in the strong sense and such that the matrix entries with
respect to the spectral decomposition of H obey the estimate
|V(t)_{m,n}|0,
p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be
arbitrarily small provided p is sufficiently large and \epsilon is small
enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the
diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where
\sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the
Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was
discussed earlier in the literature by Howland
Curvature induced toroidal bound states
Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a
particle constrained to move on the surface of a torus are calculated. A limit
on the number of bound states a torus with minor radius a and major radius R
can support is obtained. A condition for mapping constrained particle wave
functions on the torus into free particle wave functions is established.Comment: 6 pages, no figures, Late
Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example
We study a perturbed Floquet Hamiltonian depending on a coupling
constant . The spectrum is assumed to be pure point and
dense. We pick up an eigen-value, namely , and show the
existence of a function defined on such that
for all , 0 is a point of
density for the set , and the Rayleigh-Schr\"odinger perturbation series
represents an asymptotic series for the function . All ideas
are developed and demonstrated when treating an explicit example but some of
them are expected to have an essentially wider range of application.Comment: Latex, 24 pages, 51
Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula
We consider a perturbation of an ``integrable'' Hamiltonian and give an
expression for the canonical or unitary transformation which ``simplifies''
this perturbed system. The problem is to invert a functional defined on the
Lie- algebra of observables. We give a bound for the perturbation in order to
solve this inversion. And apply this result to a particular case of the control
theory, as a first example, and to the ``quantum adiabatic transformation'', as
another example.Comment: Version 8.0. 26 pages, Latex2e, final version published in J. Phys.
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