 221 Marzieh Baradaran, Pavel Exner, Jiri Lipovsky
 Magnetic ring chains with vertex coupling of a preferred orientation
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Jan 5, 22

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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 noninvariant 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 BandBerkolaiko universality holds whenever the edges are incommensurate. The magnetic field influences the probability that an energy belongs to the spectrum in the tightchain case, and also it can turn some spectral bands into infinitely degenerate eigenvalues.
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