Kagome network with vertex coupling of a preferred orientation

• URL: http://arxiv.org/abs/2106.16019v1
• Date: Wed, 30 Jun 2021 12:35:12 GMT
• Title: Kagome network with vertex coupling of a preferred orientation
• Authors: Marzieh Baradaran and Pavel Exner
• Abstract summary: We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice. The kagome lattice example shows that even in graphs with such an uncommon universality coupling spectral may hold.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at the lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of infinite number of bands, some of which may be flat; the negative one has at most three and two bands, respectively. The kagome lattice example shows that even in graphs with such an uncommon vertex coupling spectral universality may hold: if its edges are incommensurate, the probability that a randomly chosen positive number is contained in the spectrum is $\approx 0.639$.

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