• DOI:10.1007/s00220-006-0050-0
Corpus ID: 1143829

Cantor and Band Spectra for Periodic Quantum Graphs with Magnetic Fields

@article{Brning2006CantorAB,
  title={Cantor and Band Spectra for Periodic Quantum Graphs with Magnetic Fields},
  author={J. Br{\"u}ning and V. Geyler and Konstantin Pankrashkin},
  journal={Communications in Mathematical Physics},
  year={2006},
  volume={269},
  pages={87-105}
}

J. Brüning, V. Geyler, Konstantin Pankrashkin

Published 2006

Mathematics, Physics

Communications in Mathematical Physics

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band… CONTINUE READING

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