Singular continuous Cantor spectrum for magnetic quantum walks
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- Singular continuous Cantor spectrum for magnetic quantum walks
Submitted manuscript, 596 KB, PDF document
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 language | English |
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Journal | Letters in Mathematical Physics |
Volume | 110 |
Pages (from-to) | 1141–1158 |
ISSN | 0377-9017 |
DOIs | |
Publication status | Published - 2020 |
- Cantor spectrum, Discrete electromagnetism, Quantum walks, Singular continuous spectrum, Spectral theory
Research areas
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