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.
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.
There is no two dimensional analogue of Lamé's equation.
Three-Hilbert-space formulation of quantum mechanics.
Threshold scattering in two dimensions
Tightness results for laws of diffusion processes application to stochastic mechanics
Time and space complexity of reversible pebbling
This paper investigates one possible model of reversible computations, an important paradigm in the context of quantum computing. Introduced by Bennett, a reversible pebble game is an abstraction of reversible computation that allows to examine the space and time complexity of various classes of problems. We present a technique for proving lower and upper bounds on time and space complexity for several types of graphs. Using this technique we show that the time needed to achieve optimal space for...
Time and space complexity of reversible pebbling
This paper investigates one possible model of reversible computations, an important paradigm in the context of quantum computing. Introduced by Bennett, a reversible pebble game is an abstraction of reversible computation that allows to examine the space and time complexity of various classes of problems. We present a technique for proving lower and upper bounds on time and space complexity for several types of graphs. Using this technique we show that the time needed to achieve optimal space for...
Time as a quantum observable, canonically conjugated to energy, and foundations of self-consistent time analysis of quantum processes.
Time averaging for the strongly confined nonlinear Schrödinger equation