Cairo lattice with time-reversal non-invariant vertex couplings

2023/12/21 by Marzieh Baradaran, Baradaran, Marzieh, Pavel Exner +1 · 1 citation
Physics and Astronomy · #34L05 #81Q10 #81Q35 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2312.13827

openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We analyze the spectrum of a periodic quantum graph of the Cairo lattice form. The used vertex coupling violates the time reversal invariance and its high-energy behavior depends on the vertex degree parity; in the considered example both odd and even parities are involved. The presence of the former implies that the spectrum is dominated by gaps. In addition, we discuss two modifications of the model in which this is not the case, the zero limit of the length parameter in the coupling, and the sign switch of the coupling matrix at the vertices of degree three; while different they both yield the same probability that a randomly chosen positive energy lies in the spectrum.

Cited by

• A Flux-Tunable Discrete Angular Filter

Related

• Vertex coupling interpolation in quantum chain graphs
• Spectral properties of hexagonal lattices with the -R coupling
• Topologically induced spectral behavior: the example of quantum graphs
• Gaps in the spectrum of a periodic quantum graph with periodically distributed δ'-type interactions
• Quantum lattice transport along an infinitely extended perturbation