Abstract
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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Communicated by Krzysztof Gawedzki.
The research was supported by the Czech Science Foundation (GAČR) within the project 14-06818S and by the European Union with the project ‘Support for research teams on CTU’ CZ.1.07/2.3.00/30.0034.
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Exner, P., Manko, S. Spectral Properties of Magnetic Chain Graphs. Ann. Henri Poincaré 18, 929–953 (2017). https://doi.org/10.1007/s00023-016-0500-y
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DOI: https://doi.org/10.1007/s00023-016-0500-y