Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices

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Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices. / Cedzich, C.; Werner, A. H.

I: Communications in Mathematical Physics, Bind 387, Nr. 3, 2021, s. 1257-1279.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Cedzich, C & Werner, AH 2021, 'Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices', Communications in Mathematical Physics, bind 387, nr. 3, s. 1257-1279. https://doi.org/10.1007/s00220-021-04204-w

APA

Cedzich, C., & Werner, A. H. (2021). Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices. Communications in Mathematical Physics, 387(3), 1257-1279. https://doi.org/10.1007/s00220-021-04204-w

Vancouver

Cedzich C, Werner AH. Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices. Communications in Mathematical Physics. 2021;387(3):1257-1279. https://doi.org/10.1007/s00220-021-04204-w

Author

Cedzich, C. ; Werner, A. H. / Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices. I: Communications in Mathematical Physics. 2021 ; Bind 387, Nr. 3. s. 1257-1279.

Bibtex

@article{96b51a243e544e668ab0b8c49abff058,
title = "Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices",
abstract = "We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling principle. We show that for all irrational fields the absolutely continuous spectrum of these systems is empty, and prove Anderson localization for almost all (irrational) fields. This result closes a gap which was left open in the original study of electric quantum walks: a spectral and dynamical characterization of these systems for typical fields. Additionally, we derive an analytic and explicit expression for the Lyapunov exponent of this model. Making use of a connection between quantum walks and CMV matrices our result implies Anderson localization for CMV matrices with a particular choice of skew-shift Verblunsky coefficients as well as for quasi-periodic unitary band matrices.",
author = "C. Cedzich and Werner, {A. H.}",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
doi = "10.1007/s00220-021-04204-w",
language = "English",
volume = "387",
pages = "1257--1279",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices

AU - Cedzich, C.

AU - Werner, A. H.

N1 - Publisher Copyright: © 2021, The Author(s).

PY - 2021

Y1 - 2021

N2 - We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling principle. We show that for all irrational fields the absolutely continuous spectrum of these systems is empty, and prove Anderson localization for almost all (irrational) fields. This result closes a gap which was left open in the original study of electric quantum walks: a spectral and dynamical characterization of these systems for typical fields. Additionally, we derive an analytic and explicit expression for the Lyapunov exponent of this model. Making use of a connection between quantum walks and CMV matrices our result implies Anderson localization for CMV matrices with a particular choice of skew-shift Verblunsky coefficients as well as for quasi-periodic unitary band matrices.

AB - We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling principle. We show that for all irrational fields the absolutely continuous spectrum of these systems is empty, and prove Anderson localization for almost all (irrational) fields. This result closes a gap which was left open in the original study of electric quantum walks: a spectral and dynamical characterization of these systems for typical fields. Additionally, we derive an analytic and explicit expression for the Lyapunov exponent of this model. Making use of a connection between quantum walks and CMV matrices our result implies Anderson localization for CMV matrices with a particular choice of skew-shift Verblunsky coefficients as well as for quasi-periodic unitary band matrices.

UR - http://www.scopus.com/inward/record.url?scp=85115113849&partnerID=8YFLogxK

U2 - 10.1007/s00220-021-04204-w

DO - 10.1007/s00220-021-04204-w

M3 - Journal article

AN - SCOPUS:85115113849

VL - 387

SP - 1257

EP - 1279

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -

ID: 284174410