Spectrum of periodic chain graphs with time-reversal non-invariant vertex coupling

• URL: http://arxiv.org/abs/2012.14344v2
• Date: Mon, 11 Jul 2022 14:39:56 GMT
• Title: Spectrum of periodic chain graphs with time-reversal non-invariant vertex coupling
• Authors: Marzieh Baradaran, Pavel Exner, Milos Tater
• Abstract summary: We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair. We discuss the high-energy behavior of such systems and the limiting situations when one of the edges in the elementary cell of such a graph shrinks to zero.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly non-invariant with respect to time reversal. We discuss, in particular, the high-energy behavior of such systems and the limiting situations when one of the edges in the elementary cell of such a graph shrinks to zero. The spectrum depends on the topology and geometry of the graph. The probability that an energy belongs to the spectrum takes three different values reflecting the vertex parities and mirror symmetry, and the band patterns are influenced by commensurability of graph edge lengths.

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