Définition de l'intégrale de Feynman et processus à sauts
Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators.
Derivation of Hartree’s theory for mean-field Bose gases
This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of bosons with an interaction of intensity (mean-field regime). In the limit , we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation in these...
Dérivations, formes et opérateurs usuels sur les champs spinoriels des variétés différentiables de dimension paire
Développement asymptotique de la densité d'états pour des opérateurs de Schrödinger aléatoires singuliers
Développements asymptotiques dans l'approximation de Born-Oppenheimer
Développements asymptotiques des perturbations lentes de l'opérateur de Schrödinger périodique
Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
Diamagnetic behavior of sums Dirichlet eigenvalues
The Li-Yau semiclassical lower bound for the sum of the first eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.
Differential representations of dynamical oscillator symmetries in discrete Hilbert space.
Diffusion Monte Carlo method: Numerical Analysis in a Simple Case
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove...
Dirac equations with moving nuclei
Discrete spectrum of operator valued Friedrichs models
Discretized representations of harmonic variables by bilateral Jacobi operators.
Dispersive waves and caustics.
Distribution of matrix elements and level spacings for classically chaotic systems
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Do nonsingular globally bounded positon solutions exist?
Double and triple summation expressions obtained using perturbation theory.
Dynamical entropy of a non-commutative version of the phase doubling
A quantum dynamical system, mimicking the classical phase doubling map on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.