Local decay estimates for Schrödinger operators with long range potentials
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Long range scattering and modified wave operators for Hartree equations
We study the theory of scattering for the Hartree equation with long range potentials. We prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.
Long range scattering with Stark effect and almost periodic potentials.
Long-range many-body scattering.
Long-range scattering of two- and three-body quantum systems
Majoration du nombre de résonances près de l'axe réel (d'après un travail avec M. Zworski)
Mathematical Aspects of 't Hooft's Eigenvalue Problem in Two-Dimensional Quantum Chromodynamcis Part III.
Matrice de scattering et résonances associées à une orbite hétérocline
Matrices de diffusion pour l'opérateur de Schrödinger en présence d'un champ magnétique. Phénomène de Aharonov-Bohm
Multiple commutator estimates and resolvent smoothness in quantum scattering theory
N-Body quantum systems with singular potentials
New channels in three-body long-range scattering
New representations of the Poincaré group describing two interacting bosons
Non-unitary scattering and capture. II. Quantum dynamical semigroup theory
On a Class of non Linear Schrödinger Equations with non Local Interaction.
On eigenfunction expansions and scattering theory.
On non-overdetermined inverse scattering at zero energy in three dimensions
We develop the -approach to inverse scattering at zero energy in dimensions of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction of the Faddeev generalized scattering amplitude in the...
On resonances in mathematical scattering theory
On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case
We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.