Quantum graphs and microwave networks as narrow band filters for quantum and microwave devices

Abstract

We investigate properties of the transmission amplitude of quantum graphs and microwave networks composed of regular polygons such as triangles and squares. We show that for the graphs composed of regular polygons with the edges of the length $l$ the transmission amplitude displays a band of transmission suppression with some narrow peaks of full transmission. The peaks are distributed symmetrically with respect to the symmetry axis $kl=\pi$, where $k$ is the wave vector. For microwave networks the transmission peak amplitudes are reduced and their symmetry is broken due to the influence of internal absorption. We demonstrate that for the graphs composed of the same polygons but separated by the edges of length $l^{\prime }<l$ the transmission spectrum is generally not symmetric according to the axis $k{l}^{\prime }=\pi$. We also show that graphs composed of regular polygons of different size with the edges being irrational numbers are not fully chaotic and their level spacing distribution and the spectral rigidity are well described by the Berry-Robnik distributions. Moreover, the transmission spectrum of such a graph displays peaks which are very close to $1$. Furthermore, the microwave networks are investigated in the time-domain using short Gaussian pulses. In this case the delay-time distributions, though very sensitive to the internal structure of the networks, show the sequences of transmitted peaks with the amplitudes much smaller than the input one. The analyzed properties of the graphs and networks suggest that they can be effectively used to manipulate quantum and wave transport.

References in corpus (12)

• Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
• Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
• Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
• Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
• Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption
• Experimental investigation of nodal domains in the chaotic microwave rough billiard
• Non-Weyl Microwave Graphs
• Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard
• A Quantum Graph Approach to Metamaterial Design
• Hearing Euler characteristic of graphs
• The edge switch transformation in microwave networks
• A scattering model of 1D quantum wire regular polygons

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