Singular continuous Cantor spectrum for magnetic quantum walks
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- 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.
Originalsprog | Engelsk |
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Tidsskrift | Letters in Mathematical Physics |
Vol/bind | 110 |
Sider (fra-til) | 1141–1158 |
ISSN | 0377-9017 |
DOI | |
Status | Udgivet - 2020 |
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