Matrices de diffusion pour l'opérateur de Schrödinger en présence d'un champ magnétique. Phénomène de Aharonov-Bohm
Microlocalization of resonant states and estimates of the residue of the scattering amplitude
We obtain some microlocal estimates of the resonant states associated to a resonance of an -differential operator. More precisely, we show that the normalized resonant states are
Modified wave operators for nonlinear Schrödinger equations in one and two dimensions.
Modified wave operators for the derivative nonlinear Schrödinger equation.
New channels in three-body long-range scattering
Non-existence of wave operators for Stark effect Hamiltonians.
Nonlinear Scattering for Some Dispersive Equations Generalizing Benjamin-Bona-Mahony Equation.
Nonlinear Schrödinger equation on real hyperbolic spaces
Nonlinear Small Data Scattering for the Wave and Klein-Gordon Equation.
Non-unitary scattering and capture. II. Quantum dynamical semigroup theory
On a Class of non Linear Schrödinger Equations with non Local Interaction.
On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the normal derivative of the groundstate on the boundary. We then propose to use this formulation in the...
On eigenfunction expansions and scattering theory.
On Lavine's formula for time-delay.
On L...-decay and scattering for nonlinear Klein-Gordon equations.
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 poles of scattering matrices for several convex bodies
On resonant scattering for time-periodic perturbations
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.
On some elliptic transmission problems
Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of . The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically...