Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks

TL;DR

This paper experimentally explores how topological resonances relate to the Fermi golden rule in microwave networks, revealing the decay rates of states and their trajectories in the complex plane.

Contribution

It demonstrates the connection between embedded eigenvalues and topological resonances in microwave networks, providing new insights into their decay dynamics.

Findings

Embedded eigenvalues are linked to topological resonances.

Trajectories of resonances are mapped in the complex plane.

Decay rates follow the Fermi golden rule in the studied systems.

Abstract

We investigate experimentally a Fermi golden rule in two-edge and five-edge microwave networks with preserved time reversal invariance. A Fermi golden rule gives rates of decay of states obtained by perturbing embedded eigenvalues of graphs and networks. We show that the embedded eigenvalues are connected with the topological resonances of the analyzed systems and we find the trajectories of the topological resonances in the complex plane.