Singular continuous Cantor spectrum for magnetic quantum walks

C. Cedzich*, J. Fillman, T. Geib, A. H. Werner

*Corresponding author for this work

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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.

Original languageEnglish
JournalLetters in Mathematical Physics
Volume110
Pages (from-to)1141–1158
ISSN0377-9017
DOIs
Publication statusPublished - 2020

Keywords

  • Cantor spectrum
  • Discrete electromagnetism
  • Quantum walks
  • Singular continuous spectrum
  • Spectral theory

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