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arXiv · 2305.12840

Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics

Xiaodong Zhang·Weihua Zhang·Jiongning Che·Barbara Dietz
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Abstract

We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T-invariance violation and chaoticity are induced by magnetizing a ferrite disk placed at its center, which above the cutoff frequency of the first transverse-electric mode acts as a random potential. We determine a complete sequence of approx. 1000 eigenfrequencies and find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model, which interpolates between Poisson statistics expected for typical integrable systems and Gaussian unitary ensemble statistics predicted for chaotic systems with violated T invariance. Furthermore, we combine the RP model and the Heidelberg approach for quantum-chaotic scattering to construct a random-matrix model for the scattering (S) matrix of the corresponding open quantum system and show that it perfectly reproduces the fluctuation properties of the measured S matrix of the microwave resonator.

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Xiaodong Zhang, Weihua Zhang, Jiongning Che, Barbara Dietz. 2023-05-22. Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics. https://doi.org/10.1103/physreve.108.044211

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