Distortion analyticity for two-body Schrödinger operators
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Doubling properties and unique continuation at the boundary for elliptic operators with singular magnetic fields
Let u be a solution to a second order elliptic equation with singular magnetic fields, vanishing continuously on an open subset Γ of the boundary of a Lipschitz domain. An elementary proof of the doubling property for u² over balls centered at some points near Γ is presented. Moreover, we get the unique continuation at the boundary of Dini domains for elliptic operators.
Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator
We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...
Effective Hamiltonians and Quantum States
We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function solving the eikonal equation aėȧnd a probability measure solving a related transport equation.We present some elementary formal identities relating certain quantum states and . We show also how to build out of an approximate...
Effet régularisant microlocal analytique pour l’équation de Schrödinger
Effet tunnel pour des puits sous-variétés
Effet tunnel pour l'équation de Schrödinger avec champ magnétique
Effet tunnel pour l'opérateur de Schrödinger semi-classique. I
Efficient bounds for the spectral shift function
Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential.
Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.
Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Entropy and localization of eigenfunctions
Équation de Schrödinger avec champ magnétique et équation de Harper
Équation de Schrödinger en dimension 2, avec potentiel et champ magnétique périodiques. Cas d'un réseau triangulaire de puits
Équation de Schrödinger et propagation des singularités. II
Équation de Schrödinger magnétique périodique avec symétrie d'ordre six : mesure du spectre II
Équations de Schrödinger avec potentiels singuliers et à longue portée dans l'approximation de liaison forte