Magnetic ring chains with vertex coupling of a preferred orientation

TL;DR

This paper analyzes the spectral properties of a periodic quantum graph made of rings with non-invariant vertex coupling under a magnetic field, revealing how vertex parity and magnetic effects influence the spectrum.

Contribution

It introduces a detailed spectral analysis of magnetic quantum graphs with non-invariant vertex coupling, highlighting the role of vertex parity and magnetic field effects.

Findings

Vertex parity affects spectral behavior at high energies.

Incommensurate edges lead to Band-Berkolaiko universality.

Magnetic field alters spectral band structure and degeneracy.

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.