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

Effective Hamiltonians for atoms in very strong magnetic fields

We propose three effective Hamiltonians which approximate atoms in very strong homogeneous magnetic fields $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians describe $N$ electrons and a fixed nucleus where the Coulomb interaction has been replaced by $B$-dependent one-dimensional effective (vector valued) potentials but without magnetic field. Two of them are solvable in at least the one electron case. We briefly sketch how these Hamiltonians can be used to analyse the bottom of the spectrum of such atoms.Comment: 43 page

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

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

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

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

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 $q$ 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 ${\cal Z}_0$). The QCD calculation of the Generalised Factorial Moments for negative $q$ 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/

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

Effet d’un programme d’activité physique intermittent de haute intensité sur la perte de masse grasse abdominale chez la femme DT2 ménopausée

Contexte : A la ménopause, la diminution des taux d’estrogènes favorise un dépôt de masse grasse (MG) abdominal (sous-cutané et viscéral). La MG viscérale est corrélée aux maladies cardio-vasculaires (MCV). Ce risque est accentué chez les sujets présentant un diabète de type 2 (DT2).Objectif : Comparer deux modalités d’entraînement, continu de moyenne intensité (SSE) vs. intermittent de haute intensité (HIIE), sur la perte de MG abdominale (dont viscérale) chez des femmes DT2 ménopausées.Matériels et méthode : Seize femmes DT2 ménopausées (69±1ans; IMC : 31±1 kg/m²) ont été réparties aléatoirement en deux groupes. Pendant quatre mois, deux fois par semaine, 8 d’entre elles ont réalisé un entraînement SSE (40 min de pédalage à 50% de la FCmax de réserve), et 8 ont réalisé un entraînement HIIE (8s de sprint suivies de 12s de récupération active, pendant 20 min). Pré (T0) et post entraînement (T4), la composition corporelle et la MG abdominale totale ont été mesurées par DXA (Dual Energy X-ray Absorptiometry). La MG viscérale a été estimée à partir de la méthode de Martin et Jensen1. A T0 et T4, les apports énergétiques et le niveau d’activité physique ont été déterminés (questionnaires et accéléromètrie validée2 intégrée sur smartphone).Résultats : Après 16 semaines d’intervention, sans modification des apports énergétiques et du niveau d’activité physique total, une perte de MG totale et un gain de masse maigre est observé (effet temps, p<0.05). La diminution de MG abdominale est supérieure dans le groupe HIIE (0.32% ± 2.07 vs 8.32 % ± 2.19, p<0.05) et la perte de MG viscérale n’est observée que dans le groupe HIIE (p<0.05).Conclusion : L’entraînement de type HIIE apparait comme un programme alternatif intéressant chez la femme DT2 ménopausée en diminuant significativement la MG abdominale totale et viscérale