Magnetic ring chains with vertex coupling of a preferred orientation

• URL: http://arxiv.org/abs/2201.01502v1
• Date: Wed, 5 Jan 2022 09:02:10 GMT
• Title: Magnetic ring chains with vertex coupling of a preferred orientation
• Authors: Marzieh Baradaran, Pavel Exner, Jiri Lipovsky
• Abstract summary: We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links. The magnetic field influences the probability that an energy belongs to the spectrum in the tight-chain case, and also it can turn some spectral bands into infinitely eigenvalues.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time reversal and a homogeneous magnetic field perpendicular to the graph plane is present. It is shown that the vertex parity determines the spectral behavior at high energies and the Band-Berkolaiko universality holds whenever the edges are incommensurate. The magnetic field influences the probability that an energy belongs to the spectrum in the tight-chain case, and also it can turn some spectral bands into infinitely degenerate eigenvalues.

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