Singular continuous Cantor spectrum for magnetic quantum walks

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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
Publication statusAccepted/In press - 1 Jan 2020

    Research areas

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

ID: 236786930