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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1215-1254
Number of pages	40
Journal	Journal of Spectral Theory
Volume	11
Issue number	3
DOIs	https://doi.org/10.4171/JST/370
Publication status	Published - 1 Jan 2021
Externally published	Yes

Keywords

Lyapunov exponents
Quasi-periodic cocycles
Reducibility of cocycles
Smooth dynamics
Spectral theory

Access to Document

10.4171/JST/370

Cite this

@article{aec3b0a01e3441f1a46a27e635b06a72,

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",

language = "English",

volume = "11",

pages = "1215--1254",

journal = "Journal of Spectral Theory",

issn = "1664-039X",

number = "3",

}

TY - JOUR

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

AU - Bjerklöv, Kristian

AU - Krikorian, Raphaël

PY - 2021/1/1

Y1 - 2021/1/1

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this