On the applications of a new technique to solve linear differential equations, with and without source.
On the completeness in three body scattering
On the computation of bounds for low energy Compton scattering parameters : proof of a conjecture
On the derivation of the Gross-Pitaevskii equation
This article reflects in its content the talk the author gave at the XVII Congresso dellUnione Matematica Italiana, held in Milano, 8-13 September 2003. We review about some recent results on the problem of deriving the Gross-Pitaevskii equation in dimension one from the dynamics of a quantum system with a large number of identical bosons. We explain the motivations for some peculiar choices (shape of the interaction potential, scaling, initial datum). Open problems are pointed out and difficulties...
On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
On the Scattering Matrix for N-Particle Hamiltonians
On the scattering theory for quantum dynamical semigroups
On the structure of the wave operators in one dimensional potential scattering.
On trace theorems for pseudo-differential operators
Opérateurs de temps-retard dans la théorie de la diffusion
Pole-factorization theorem in quantum electrodynamics
Prolongement méromorphe de la matrice de diffusion pour les problèmes à corps à longue portée
Prolongement méromorphe de la matrice de diffusion pour les problèmes à corps à longue portée
Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée
Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée
Propagation and local-decay properties for long-range scattering of quantum three-body systems
Propagation estimates for Dirac operators and application to scattering theory
In this paper, we prove propagation estimates for a massive Dirac equation in flat spacetime. This allows us to construct the asymptotic velocity operator and to analyse its spectrum. Eventually, using this new information, we are able to obtain complete scattering results; that is to say we prove the existence and the asymptotic completeness of the Dollard modified wave operators.
Propagation of singularities in many-body scattering
Propagation of singularities in many-body scattering in the presence of bound states
In these lecture notes we describe the propagation of singularities of tempered distributional solutions of , where is a many-body hamiltonian , , , and is not a threshold of , under the assumption that the inter-particle (e.g. two-body) interactions are real-valued polyhomogeneous symbols of order (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the...