Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates

International audienceThe aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, \textit{a priori} estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper

Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations

International audienceThis paper addresses the construction of different families of absorbing boundary conditions for the one- and two-dimensional Schrödinger equation with a general variable nonlinear potential. Various semi-discrete time schemes are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbing boundary conditions and associated schemes to analyze their accuracy and efficiency

Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. Part II: Discretization and numerical results

International audienceFour families of ABCs where built in [5] for the two- dimensional linear Schr ̈odinger equation with time and space depen- dent potentials and for general smooth convex fictitious surfaces. The aim of this paper is to propose some suitable discretization schemes of these ABCs and to prove some semi-discrete stability results. Fur- thermore, the full numerical discretization of the corresponding initial boundary value problems is considered and simulations are provided to compare the accuracy of the different ABCs

Numerical Solution of Time-Dependent Nonlinear Schrödinger Equations Using Domain Truncation Techniques Coupled With Relaxation Scheme

International audienceThe aim of this paper is to compare different ways for truncating unbounded domains for solving general nonlinear one- and two-dimensional Schrödinger equations. We propose to analyze Complex Absorbing Potentials, Perfectly Matched Layers and Absorbing Boundary Conditions. The time discretization is made by using a semi-implicit relaxation scheme which avoids any fixed point procedure. The spatial discretization involves finite element methods. We propose some numerical experiments to compare the approaches

Thermodynamics of the vortex liquid in heavy ion-irradiated superconductors

It is shown that the large effect of heavy ion-irradiation on the thermodynamical properties of the anisotropic superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ extends well into the superconducting fluctuation regime. The presence of the induced amorphous columnar defects shifts the specific heat maximum at the normal-to-superconducting transition. This effect is similar to that recently put into evidence in cubic K$_{x}$Ba$_{1-x}$BiO$_{3}$ ($x \simeq 0.35$). In both compounds, vortex pinning manifests itself as a sharp angular dependence of the \em equilibrium \rm torque. In YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, pinning by the defects appears at the temperature $T_{C_{p}}^{max}$ of the specific heat maximum, well above the magnetic irreversibility line $T_{irr}(H)$. In isotropic K$_{x}$Ba$_{1-x}$BiO$_{3}$, the onset of the pinning-related torque anomaly tracks the onset of the specific heat anomaly and the irreversibility line. In YBa$_{2}$Cu$_{3}$O$_{7-\delta}$, fluctuations of the amplitude of the order parameter (and not vortex line wandering) are ultimately responsible for the vanishing of pinning. In K$_{x}$Ba$_{1-x}$BiO$_{3}$, vortex pinning disappears only at the superconducting-to-normal transition. The results indicate that in both compounds, the pinning energy at the ``Bose glass'' transition is large with respect to the total free energy gain in the superconducting state. By implication, the mechanism of this latter transition should be reconsidered.Comment: 9 pages, 9 figures, resubmitted to PRB 23-09-200

Probing weak force induced parity violation by high resolution mid-infrared molecular spectroscopy

To date no experiment has reached the level of sensitivity required to observe weak nuclear force induced parity violation (PV) energy differences in chiral molecules. In this paper, we present the approach, adopted at Laboratoire de Physique des Lasers (LPL), to measure frequency differences in the vibrational spectrum of enantiomers. We review different spectroscopic methods developed at LPL leading to the highest resolutions, as well as 20 years of CO2 laser stabilization work enabling such precise measurements. After a first attempt to observe PV vibrational frequency shifts using sub-Doppler saturated absorption spectroscopy in a cell, we are currently aiming at an experiment based on Doppler-free two-photon Ramsey interferometry on a supersonic beam. We report on our latest progress towards observing PV with chiral organo-metallic complexes containing a heavy rhenium atom

10 um wavefront spatial filtering: first results with chalcogenide fibers

Wavefront cleaning by single-mode fibers has proved to be efficient in optical-infrared interferometry to improve calibration quality. For instance, the FLUOR instrument has demonstrated the capability of fluoride glass single-mode fibers in this respect in the K and L bands. New interferometric instruments developped for the mid-infrared require the same capability for the 8-12 um range. We have initiated a program to develop single-mode fibers in the prospect of the VLTI mid-infrared instrument MIDI and of the ESA/DARWIN and NASA/TPF missions that require excellent wavefront quality. In order to characterize the performances of chalcogenide fibers we are developping, we have set up an experiment to measure the far-field pattern radiated at 10 um. In this paper, we report the first and promising results obtained with this new component.Comment: Conference "Interferometry for Optical Astronomy II", SPIE 200

Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

International audienceWe propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrö\-din\-ger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to $N$-dimensional stationary Schrödinger equations

Intégration spatiale des frontaliers à travers les activités quotidiennes. Le cas de la région métropolitaine luxembourgeoise.

National audienceThe number of cross-border workers in Luxembourg has steadily increased for over thirty years. The purpose of this article is to measure the integration of cross-border workers in Luxembourg by using the concepts of Time Geography and living spaces. The analysis focuses on the spatial and temporal organisation of the daily activities and their sequential location on both sides of the border. Thus, measuring living spaces and trip chains of cross-border workers represents the core of the methodological and analytical support. The juxtaposition of these trip chains with the living spaces allows identifying and characterising the degree of spatial integration of cross-border workers in Luxembourg. Apart from cross-border workers who are mainly shifting between their working place and their residence, the first results show a varying integration degreeLe nombre de travailleurs frontaliers au Luxembourg augmente de manière constante depuis 30 ans. Le but de cet article est de questionner l'intégration de ces frontaliers au Luxembourg au moyen de concepts issus de la Time Geography, en particulier celui des espaces de vie. Il s'agit d'analyser la répartition spatiale des activités quotidiennes, leur succession dans le temps et leur localisation par rapport à la frontière. Ainsi, la mesure des espaces de vie et des chaînes de déplacement des frontaliers constitue le principal support méthodologique et analytique pour identifier et caractériser le degré d'intégration spatiale de ces actifs au Luxembourg. Outre les simples déplacements domicile-travail qui n'engendrent pas d'activités secondaires, les principaux résultats témoignent de quatre autres types d'intégration spatiale plus ou moins importants