N-Body quantum systems with singular potentials
New channels in three-body long-range scattering
On eigenfunction expansions and scattering theory.
On resonances in mathematical scattering theory
On the completeness in three body scattering
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 Scattering Matrix for N-Particle Hamiltonians
Prolongement méromorphe de la matrice de diffusion pour les problèmes à corps à longue portée
Propagation and local-decay properties for long-range scattering of quantum three-body systems
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...
Properties of the scattering amplitude for electron-atom collisions
Radiation conditions and scattering theory for -particle quantum systems
Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture. II
Scattering for a dispersive charge transfer model
Scattering theory for 3-particle systems in constant magnetic fields : dispersive case
We develop a scattering theory for quantum systems of three charged particles in a constant magnetic field. For such systems, we generalize our earlier results in that we make no additional assumptions on the electric charges of subsystems. The main difficulty is the analysis of the scattering channels corresponding to the motion of the bound states of the neutral subsystems in the directions transversal to the field. The effective kinetic energy of this motion is given by certain dispersive Hamiltonians;...
Scattering theory for plektons in 2 + 1 dimensions
Semiclassical resolvent estimates
Semiclassical resolvent estimates for two and three-body Schrödinger operators
Shadow scattering by magnetic fields in two dimensions