Singular continuous Cantor spectrum for magnetic quantum walks

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Standard

Singular continuous Cantor spectrum for magnetic quantum walks. / Cedzich, C.; Fillman, J.; Geib, T.; Werner, A. H.

In: Letters in Mathematical Physics, Vol. 110, 2020, p. 1141–1158.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Cedzich, C, Fillman, J, Geib, T & Werner, AH 2020, 'Singular continuous Cantor spectrum for magnetic quantum walks', Letters in Mathematical Physics, vol. 110, pp. 1141–1158. https://doi.org/10.1007/s11005-020-01257-1

APA

Cedzich, C., Fillman, J., Geib, T., & Werner, A. H. (2020). Singular continuous Cantor spectrum for magnetic quantum walks. Letters in Mathematical Physics, 110, 1141–1158. https://doi.org/10.1007/s11005-020-01257-1

Vancouver

Cedzich C, Fillman J, Geib T, Werner AH. Singular continuous Cantor spectrum for magnetic quantum walks. Letters in Mathematical Physics. 2020;110:1141–1158. https://doi.org/10.1007/s11005-020-01257-1

Author

Cedzich, C. ; Fillman, J. ; Geib, T. ; Werner, A. H. / Singular continuous Cantor spectrum for magnetic quantum walks. In: Letters in Mathematical Physics. 2020 ; Vol. 110. pp. 1141–1158.

Bibtex

@article{1f66a79624174e939d7a584b76d99e48,
title = "Singular continuous Cantor spectrum for magnetic quantum walks",
abstract = "In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure and its type depend sensitively on the value of the magnetic flux Φ : While for Φ / (2 π) rational the spectrum is known to consist of bands, we show that for Φ / (2 π) irrational, the spectrum is a zero-measure Cantor set and the spectral measures have no pure point part.",
keywords = "Cantor spectrum, Discrete electromagnetism, Quantum walks, Singular continuous spectrum, Spectral theory",
author = "C. Cedzich and J. Fillman and T. Geib and Werner, {A. H.}",
year = "2020",
doi = "10.1007/s11005-020-01257-1",
language = "English",
volume = "110",
pages = "1141–1158",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Singular continuous Cantor spectrum for magnetic quantum walks

AU - Cedzich, C.

AU - Fillman, J.

AU - Geib, T.

AU - Werner, A. H.

PY - 2020

Y1 - 2020

N2 - In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure and its type depend sensitively on the value of the magnetic flux Φ : While for Φ / (2 π) rational the spectrum is known to consist of bands, we show that for Φ / (2 π) irrational, the spectrum is a zero-measure Cantor set and the spectral measures have no pure point part.

AB - In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure and its type depend sensitively on the value of the magnetic flux Φ : While for Φ / (2 π) rational the spectrum is known to consist of bands, we show that for Φ / (2 π) irrational, the spectrum is a zero-measure Cantor set and the spectral measures have no pure point part.

KW - Cantor spectrum

KW - Discrete electromagnetism

KW - Quantum walks

KW - Singular continuous spectrum

KW - Spectral theory

UR - http://www.scopus.com/inward/record.url?scp=85079463846&partnerID=8YFLogxK

U2 - 10.1007/s11005-020-01257-1

DO - 10.1007/s11005-020-01257-1

M3 - Journal article

AN - SCOPUS:85079463846

VL - 110

SP - 1141

EP - 1158

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -

ID: 236786930