Propagation of waves in a randomly stratified medium: an inverse problem.
Properties of normal boundary problems for elliptic even-order systems
Property C for ordinary differential equations and applications to inverse scattering.
Propriétés asymptotiques de l'équation de la chaleur sur une variété compacte
Propriétés génériques des rayons réfléchissants et applications aux problèmes spectraux
Propriétés spectrales d'opérateurs pseudodifférentiels
Pseudo-differential operators with positive symbols
Pseudospectrum for differential operators
Puits de potentiel généralisés et asymptotique semi-classique
Puits multiples (d'après des travaux avec B. Helffer)
Puits multiples en limite semi-classique. II. Interaction moléculaire. Symétries. Perturbation
Puits multiples en mécanique semi-classique VI. (Cas des puits sous-variétés)
Puits multiples pour l'opérateur de Dirac
Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite ?
Classically, Hardy’s inequality enables to estimate the spectral gap of a one-dimensional diffusion up to a factor belonging to . The goal of this paper is to better understand the latter factor, at least in a symmetric setting. In particular, we will give an asymptotical criterion implying that its value is exactly 4. The underlying argument is based on a semi-explicit functional for the spectral gap, which is monotone in some rearrangement of the data. To find it will resort to some regularity...
Quantification et approximations semi-classiques
Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.
We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on -forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of and solves efficiently the question of weakly resonant wells.
Quantum decay rates in chaotic scattering
Quantum diffusion and generalized Rényi dimensions of spectral measures
We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order at time for the state defined by . We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure associated to the hamiltonian and the state . We especially concentrate on continuous models.
Quantum graph spectra of a graphyne structure
We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.
Quantum scattering by external metrics and Yang-Mills potentials