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arXiv:2601.11212

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

Xiaodong Zhang, Jiongning Che, Barbara Dietz

nlin.CDquant-phSubmitted Jan 16, 2026• Announced Jan 19, 2026

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.

Comments: Corresponding author: Barbara Dietz

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Q

cavity modes in a wide range of frequency as the cavity deformation increased. By employing an internal parameter, we were able to obtain a mode-dynamics diagram at a given deformation, showing avoided crossings between different mode groups, and could directly observe the coupling strengths induced by ray chaos among encountering modes. We also show that the observed mode-dynamics diagrams reflect the underlying classical ray dynamics in the phase space.