Annales Henri Poincaré

, Volume 18, Issue 3, pp 929–953 | Cite as

Spectral Properties of Magnetic Chain Graphs

  • Pavel ExnerEmail author
  • Stepan Manko


We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under the influence of a magnetic field assuming a \({\delta}\)-coupling at the points where the rings touch. We start with the situation when the system has a translational symmetry and analyze spectral consequences of perturbations of various kind, such as a local change of the magnetic field, of the coupling constant, or of a ring circumference. A particular attention is paid to weak perturbations, both local and periodic; for the later, we prove a version of Saxon–Hutner conjecture.


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.PragueCzech Republic
  2. 2.DěčínCzech Republic

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