Related Experiment Video
Updated: Jul 10, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble
Xiaodong Zhang1, Weihua Zhang1,2, Jiongning Che1
1Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.
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 ≃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 Tinvariance. 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.
Related Concept Videos
Wald-Wolfowitz Runs Test II
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
Poisson Probability Distribution
The...
Statistical Hypothesis Testing
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
On...
Expected Frequencies in Goodness-of-Fit Tests
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...

