Experimental study of coupled quantum billiards with integrable and chaotic classical dynamics and test of a special Rosenzweig-Porter model

TL;DR

This study experimentally investigates the spectral properties of coupled quantum billiards with different classical dynamics and validates a special Rosenzweig-Porter model to describe the coupling effects and eigenstate mixing.

Contribution

It introduces a novel experimental setup of coupled quantum billiards with mixed classical dynamics and demonstrates the model's effectiveness in describing spectral properties and coupling strength.

Findings

Model accurately describes experimental spectral data

Eigenmode overlap increases with coupling, causing state mixing

Spectral properties transition towards chaotic behavior with stronger coupling

Abstract

We report on the experimental study of the spectral properties of quantum systems consisting of two quantum billiards (QBs), one with chaotic, the other one with integrable classical dynamics, that are coupled to each other via an opening in a common wall. They are compared to those of a special case of the Rosenzweig-Porter model with random matrices composed of two diagonal blocks modeling the spectral properties of the QBs, that are coupled with a tunable parameter. We demonstrate that this model is suitable for the description of the experimental data and thus may be employed to determine the strength of the coupling. It results from the increasing overlap of eigenmodes in the QBs penetrating through the opening into the other one, leading to a mixing of their eigenstates, and the breaking of the symmetry present in the QB with integrable dynamics. This implicates deviations of the spectral properties from those of typical quantum systems with integrable and chaotic dynamics, respectively, and approaches those of a fully chaotic system for sufficiently large coupling strength. In contrast in previous studies the transition from integrable to chaotic dynamics was induced by introducing a random potential of increasing strength into such a QB and applicability of a variant of the Rosenzweig-Porter model was tested.