Singular continuous Cantor spectrum for magnetic quantum walks
Research output: Contribution to journal › Journal article › Research › peer-review
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.
|Journal||Letters in Mathematical Physics|
|Publication status||Accepted/In press - 1 Jan 2020|
- Cantor spectrum, Discrete electromagnetism, Quantum walks, Singular continuous spectrum, Spectral theory