Experimental Study of Quantum Graphs with Simple Microwave Networks: Non-Universal Features

Abstract

Quantum graphs provide a setting to test the hypothesis that all ray-chaotic systems show universal wave chaotic properties. Here, an experimental setup consisting of a microwave coaxial cable network is used to simulate quantum graphs. The networks which are large compared to the wavelength, are constructed from coaxial cables connected by T junctions. The distributions of impedance statistics are obtained from experiments on an ensemble of tetrahedral networks. The random coupling model (RCM) is applied in an attempt to uncover the universal statistical properties of the system. Deviations from RCM predictions have been observed in that the statistics of diagonal and off-diagonal impedance elements are different. It is argued that because of the small finite-size quantum graphs utilized here there will be non-universal results.

Perfect absorption in complex scattering systems with or without hidden symmetries

“…33,39 ) using semiclassics and their origin has been traced back to the presence of short periodic orbits that are trapped along individual bonds of the graph. Subsequent theoretical studies [28][29][30][31][32]34 have further established conditions under which RMT universality can be restored, while experimental implementations of graphs in the microwave realm 20,[40][41][42][43] have provided additional evidence of the origin of these deviations [44][45][46] . Thus our platform, being a typical complex scattering system without any geometric symmetries and with controlled TR symmetries, and demonstrating both the extreme sensitivity to perturbations and typical deviations from universal statistical behavior 45 -due to system-specific features-is an ideal surrogate for testing the viability of CPA protocols in real-world scattering systems.…”

“…Our experiment utilizes a tetrahedral microwave graph formed by coaxial cables and Tee-junctions 46,48 . A variable attenuator is attached to one internal node of the graph (see Fig.…”

Scattering statistics in nonlinear wave chaotic systems

“…The success of the principles underlying the RCM has been experimentally verified in linear wave chaotic systems including microwave systems [48][49][50] and acoustic systems [51][52][53][54][55], from 1D quantum graphs [56][57][58], 2D electromagnetic billiards [14,15,43,59], and 3D cavities [60][61][62][63]. Based on its success and flexibility, it is of great interest to extend the RCM to other systems.…”

A trace formula for metric graphs with piecewise constant potentials and multi-mode graphs

“…Metric graphs with a self-adjoint wave operator, known as quantum graphs, turned out to be a paradigmatic model in the physics of complex wave systems (quantum chaos [2,3]) and in mathematical spectral theory [4]. At the same time the model was applied to wave properties of actual physical networks such as e.g., optical fibers, microwave cables or waveguides [5][6][7][8][9][10][11]. For most of these applications the quantum graph model suffices, in spite of its being a drastic idealization of the complete physical system: It is limited to complex-valued scalar wave functions that propagate freely along the edges and their scattering in the junctions (vertices) are provided by appropriate boundary conditions.…”