Resonances for large one-dimensional “ergodic” systems

Klopp, Frédéric

doi:10.2140/apde.2016.9.259

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Resonances for large one-dimensional “ergodic” systems

Frédéric Klopp

Vol. 9 (2016), No. 2, 259–352

DOI: 10.2140/apde.2016.9.259

Abstract

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.

Keywords

resonances, random operators, periodic operators

Mathematical Subject Classification 2010

Primary: 35B34, 47B80, 47H40, 60H25, 82B44

Milestones

Received: 2 October 2012

Revised: 29 August 2015

Accepted: 30 January 2016

Published: 24 March 2016

Authors

Frédéric Klopp
Institute de Mathématiques Jussieu — Paris Rive Gauche, UMR 7586, CNRS Université Pierre et Marie Curie Case 186, 4 place Jussieu 75252 Paris France

Vol. 9, No. 2, 2016