Effet tunnel pour des puits sous-variétés
Effet Zeeman pour un électron de Dirac
Effets dispersifs dans les équations de Schrödinger et de Vlasov
Eigenfunction expansions of functions describing systems with symmetries.
Eigenfunctions of the laplacian, quantum chaos, and computation
Eigenmodes of the damped wave equation and small hyperbolic subsets
We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of -damped stationary solutions cannot be completely concentrated in small neighborhoods of a small fixed hyperbolic subset made of -damped trajectories of the geodesic flow.The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues...
Eigenvalue asymptotics for the Dirac operator in strong constant magnetic fields.
Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields
We consider the Pauli operator selfadjoint in , . Here , , are the Pauli matrices, is the magnetic potential, is the coupling constant, and is the electric potential which decays at infinity. We suppose that the magnetic field generated by satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case , its direction is constant. We investigate the asymptotic behaviour as of the number of the eigenvalues of smaller than...
Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.
Eigenvalue distribution of random operators and matrices
Electronic properties of disclinated nanostructured cylinders
The electronic structure of the nanocylinder is investigated. Two cases of this kind of the nanostructure are explored: the defect-free nanocylinder and the nanocylinder whose geometry is perturbed by 2 heptagonal defects lying on the opposite sides. The characteristic quantity which is of our interest is the local density of states. To calculate it, the continuum gauge field-theory model will be used. In this model, the Dirac-like equation is solved on a curved surface. This procedure was used...
Elementary linear algebra for advanced spectral problems
We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...
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 magnétique périodique avec symétrie d'ordre six : mesure du spectre II
Équations de champ moyen pour la dynamique quantique d’un grand nombre de particules
L’objet de cet exposé est de montrer comment l’évolution de Schrödinger pour le problème à corps quantique est approchée, lorsque tend vers l’infini, dans un régime convenable, par une évolution non-linéaire en dimension trois d’espace. On traitera le cas des bosons, qui conduit à l’équation de Schrödinger-Poisson, et celui des fermions, qui débouche sur le système de Hartree-Fock.
Équations de champs non linéaires: Des solutions non nécessairement bornées
Équations de Schrödinger avec potentiels singuliers et à longue portée dans l'approximation de liaison forte
Équations non linéaires du type Thomas-Fermi
Equidistribution of cusp forms on
We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on . This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on .