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Quantum Circuit Design Gate Engineering

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

arXiv
Authors: Marzieh Baradaran, Pavel Exner, Milos Tater

Year

2020

Paper ID

482

Status

Preprint

Abstract Read

~2 min

Abstract Words

115

Citations

N/A

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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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.14344 [2] arXiv https://arxiv.org/abs/2012.14344 [3] Publisher https://arxiv.org/abs/2012.14344

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