Coexistence of absolutely continuous and pure point spectrum for kicked quasiperiodic potentials

Kristian Bjerklöv; Raphaël Krikorian

doi:10.4171/JST/370

Coexistence of absolutely continuous and pure point spectrum for kicked quasiperiodic potentials

Kristian Bjerklöv
, Raphaël Krikorian

KTH Royal Institute of Technology
CY Cergy Paris Université

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We introduce a class of real analytic "peaky"potentials for which the corresponding quasiperiodic 1D-Schrödinger operators exhibit, for quasiperiodic frequencies in a set of positive Lebesgue measure, both absolutely continuous and pure point spectrum.

langue originale	Anglais
Pages (de - à)	1215-1254
Nombre de pages	40
journal	Journal of Spectral Theory
Volume	11
Numéro de publication	3
Les DOIs	https://doi.org/10.4171/JST/370
état	Publié - 1 janv. 2021
Modification externe	Oui

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10.4171/JST/370

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title = "Coexistence of absolutely continuous and pure point spectrum for kicked quasiperiodic potentials",

abstract = "We introduce a class of real analytic {"}peaky{"}potentials for which the corresponding quasiperiodic 1D-Schr{\"o}dinger operators exhibit, for quasiperiodic frequencies in a set of positive Lebesgue measure, both absolutely continuous and pure point spectrum.",

keywords = "Lyapunov exponents, Quasi-periodic cocycles, Reducibility of cocycles, Smooth dynamics, Spectral theory",

author = "Kristian Bjerkl{\"o}v and Rapha{\"e}l Krikorian",

note = "Publisher Copyright: {\textcopyright} 2021 European Mathematical Society.",

year = "2021",

month = jan,

day = "1",

doi = "10.4171/JST/370",

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journal = "Journal of Spectral Theory",

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T1 - Coexistence of absolutely continuous and pure point spectrum for kicked quasiperiodic potentials

AU - Bjerklöv, Kristian

AU - Krikorian, Raphaël

PY - 2021/1/1

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N2 - We introduce a class of real analytic "peaky"potentials for which the corresponding quasiperiodic 1D-Schrödinger operators exhibit, for quasiperiodic frequencies in a set of positive Lebesgue measure, both absolutely continuous and pure point spectrum.

AB - We introduce a class of real analytic "peaky"potentials for which the corresponding quasiperiodic 1D-Schrödinger operators exhibit, for quasiperiodic frequencies in a set of positive Lebesgue measure, both absolutely continuous and pure point spectrum.

KW - Lyapunov exponents

KW - Quasi-periodic cocycles

KW - Reducibility of cocycles

KW - Smooth dynamics

KW - Spectral theory

U2 - 10.4171/JST/370

DO - 10.4171/JST/370

M3 - Article

AN - SCOPUS:85116839193

SN - 1664-039X

VL - 11

SP - 1215

EP - 1254

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 3

ER -

Coexistence of absolutely continuous and pure point spectrum for kicked quasiperiodic potentials

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