TY - JOUR
T1 - Singular continuous Cantor spectrum for magnetic quantum walks
AU - Cedzich, C.
AU - Fillman, J.
AU - Geib, T.
AU - Werner, A. H.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Cantor spectrum
KW - Discrete electromagnetism
KW - Quantum walks
KW - Singular continuous spectrum
KW - Spectral theory
UR - http://www.scopus.com/inward/record.url?scp=85079463846&partnerID=8YFLogxK
U2 - 10.1007/s11005-020-01257-1
DO - 10.1007/s11005-020-01257-1
M3 - Journal article
AN - SCOPUS:85079463846
VL - 110
SP - 1141
EP - 1158
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
SN - 0377-9017
ER -