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

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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Cited by in corpus (7)

• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• Long-range spectral statistics of the Rosenzweig-Porter model
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Relaxation Fluctuations of Correlation Functions: Spin and Random Matrix Models