The theory of systems with internal degrees of freedom
The time-dependent Born-Oppenheimer approximation
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.
The Tomita operator for the free scalar field
The topology of the Yang-Mills theory over torus
The trajectory-coherent approximation and the system of moments for the Hartree type equation.
The tripartite separability of density matrices of graphs.
The Uncertainty Principle: A Mathematical Survey.
The Virasoro algebra and some exceptional Lie and finite groups.
The wall of the cave
The wave equation in random domains : localization of the normal modes in the small frequency region
The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
The weak coupling limit without rotating wave approximation
The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
In this paper we are interested in constructing WKB approximations for the nonlinear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.
The Yang-Baxter and pentagon equation
Théorie classique des champs en interaction : théorie de jauge et interprétation géométrique
Théorie de la diffusion pour le modèle de Nelson et problème infrarouge
Nous considérons dans cet exposé la théorie de la diffusion pour des modèles de Pauli-Fierz sans masse divergents infrarouge. Nous montrons que les représentations CCR obtenues a partir des champs asymptotiques contiennent des secteurs cohérents décrivant un nombre infini de bosons asymptotiquement libres. Nous formulons quelques conjectures qui conduisent a une notion bien définie de sections efficaces inclusives et non inclusives pour les Hamiltoniens de Pauli-Fierz. Finalement nous donnons une...
Théorie de la diffusion pour le modèle en théorie des champs
Théorie de la diffusion pour un atome couplé à un champ quantique
Théorie de la diffusion quantique pour des perturbations à longue et courte portée du champ magnétique
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.