 20109 Marzieh Baradaran, Pavel Exner, and Milos Tater
 Spectrum of periodic chain graphs with timereversal noninvariant vertex coupling
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Dec 28, 20

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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 noninvariant with respect to time reversal. We discuss, in particular, the highenergy 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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