Impuretés dans une structure périodique
Localisation pour des opérateurs de Schrödinger aléatoires dans : un modèle semi-classique
Dans , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...
Étude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique
Asymptotiques de Lifshitz
Cet exposé a pour but de présenter des résultats récents de l’auteur concernant les asymptotiques de Lifshitz pour des perturbations aléatoires d’opérateurs de Schrödinger périodiques. Certains de ces résultats ont été obtenus en collaboration avec T. Wolff.
Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase
In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in []. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of []. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...
Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators
Valeurs propres et résonances au voisinage d'un seuil
Renormalization of exponential sums and matrix cocycles
In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics
Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1
Opérateurs de Schrödinger quasi-périodiques adiabatiques : Interactions entre les bandes spectrales d’un opérateur périodique
This paper is devoted to the description of our recent results on the spectral behavior of one-dimensional adiabatic quasi-periodic Schrödinger operators. The specific operator we study is a slow periodic perturbation of an incommensurate periodic Schrödinger operator, and we are interested in energies where the perturbation creates a strong interaction between two consecutive bands of the background periodic operator. We describe the location of the spectrum and its nature and discuss the various...
Lifshitz tails for some non monotonous random models
In this talk, we describe some recent results on the Lifshitz behavior of the density of states for non monotonous random models. Non monotonous means that the random operator is not a monotonous function of the random variables. The models we consider will mainly be of alloy type but in some cases we also can apply our methods to random displacement models.
The width of resonances for slowly varying perturbations of one-dimensional periodic Schrödinger operators
Spectral statistics for random Schrödinger operators in the localized regime
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy in the localized phase. Assume the density of states function is not too flat near . Restrict it to some large cube . Consider now , a small energy interval centered at that asymptotically contains infintely many eigenvalues when the volume of the cube grows to infinity. We prove that, with probability one in the large volume...
The integrated density of states for an interacting multiparticle homogeneous model and applications to the Anderson model.
Page 1