Narrow peaks of full transmission in simple quantum graphs

Abstract

This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple diamond graphs, and two hexagonal graphs in which the vertices are all of degree 3, and investigate their transmission coefficients. In particular, we identified regions in which the transmission is fully suppressed. We also considered the transmission coefficients of some series and parallel arrangements of the two basic graphs, with the vertices still preserving the degree 3 condition, and then identified specific series and parallel compositions that allow for windows of no transmission. Inside some of these windows, we found very narrow peaks of full transmission, which are consequences of constructive quantum interference. Possibilities of practical use as the experimental construction of devices of current interest to control and manipulate quantum transmission are also discussed.

arXiv comment9 pages, 10 figures, minor corrections, matches published version

References in corpus (15)

• The electronic properties of graphene
• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control
• Experimental simulation of quantum graphs by microwave networks
• Transport inefficiency in branched-out mesoscopic networks: An analog of the Braess paradox
• Topological Resonances in Scattering on Networks (Graphs)
• Non-Weyl Microwave Graphs
• Complex active optical networks as a new laser concept
• Green's function approach for quantum graphs: an overview
• Quantum graphs where back-scattering is prohibited
• Braess paradox at the mesoscopic scale
• The LANER: optical networks as complex lasers
• Universal Braess paradox in open quantum dots
• Unitary equivalence between the Green's function and Schrödinger approaches for quantum graphs

Cited by in corpus (10)

• Entanglement formation in continuous-variable random quantum networks
• Use of Transmission and Reflection Complex Time Delays to Reveal Scattering Matrix Poles and Zeros: Example of the Ring Graph
• Simple quantum graphs proposal for quantum devices
• Quantum graphs and microwave networks as narrow band filters for quantum and microwave devices
• Average scattering entropy of quantum graphs
• Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs
• Quantum transport in randomized quantum graphs
• Knots and signal transmission in topological quantum devices
• A Flux-Tunable Discrete Angular Filter
• Scattering entropies of quantum graphs with several channels