Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance

TL;DR

This study uses microwave waveguide systems to experimentally model quantum graphs, analyzing spectral and wave function properties under preserved and partially violated time-reversal invariance, with implications for quantum chaos and scattering theory.

Contribution

It provides experimental insights into microwave waveguide graphs as models for quantum graphs, including the effects of time-reversal invariance violation on spectral and scattering properties.

Findings

Spectral properties align with predictions for quantum chaotic systems.

Wave functions can be experimentally determined and show characteristic features.

Scattering matrix properties are consistent with random matrix theory models.

Abstract

We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schr\"odinger equation with boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wavenumber and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the frame work of random matrix theory for quantum chaotic scattering systems.