Vol. 9, No. 2, 2016

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Resonances for large one-dimensional “ergodic” systems

Frédéric Klopp

Vol. 9 (2016), No. 2, 259–352

The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models, both on a half-line and on the whole line, we study the distributions of the resonances in the limit when the size of the box goes to infinity. For periodic and random potentials, we analyze how the spectral theory of the limit operator influences the distribution of the resonances.

Dans cet article, nous étudions les résonances d’un système unidimensionnel plongé dans un potentiel qui est la restriction à un grand intervalle d’un potentiel ergodique. Pour des modèles discrets sur la droite et la demie droite, nous étudions la distribution des résonances dans la limite de la taille de boîte infinie. Pour des potentiels périodiques et aléatoires, nous analysons l’influence de la théorie spectrale de l’opérateur limite sur la distribution des résonances.

resonances, random operators, periodic operators
Mathematical Subject Classification 2010
Primary: 35B34, 47B80, 47H40, 60H25, 82B44
Received: 2 October 2012
Revised: 29 August 2015
Accepted: 30 January 2016
Published: 24 March 2016
Frédéric Klopp
Institute de Mathématiques Jussieu — Paris Rive Gauche, UMR 7586, CNRS
Université Pierre et Marie Curie
Case 186, 4 place Jussieu
75252 Paris