Universal Frequency Correlations and Recurrence Statistics of Complex Impedance Matrices
arXiv:2508.16563 · doi:10.12693/APhysPolA.148.S49
Abstract
Linear electromagnetic wave scattering systems can be characterized by an impedance matrix that relates the voltages and currents at the ports of the system. When the system size becomes greater than the wavelength of the fields involved, the impedance matrix becomes a complicated function of the details of the system, in which case a statistical model, such as the Random Coupling Model (RCM) becomes useful. The statistics of the elements of the RCM impedance matrix depend on the excitation frequency, the spectral density of the modes of the enclosed system volume, the average loss factor (Q^{-1}) of the system, and the properties of the coupling ports as given by their radiation impedances. In this paper, properties of the elements of impedance matrices are explored numerically and experimentally. These include the two point frequency correlation functions for the complex impedance of elements and the expected difference in frequencies between which impedance values are approximately repeated. Universal scaling arguments are then given for these quantities, hence these results are generic for all sufficiently complicated scattering systems, including acoustic and optical systems. The experimental data presented in this paper come from microwave graphs, billiards, and three-dimensional cavities with embedded tunable perturbers such as metasurfaces. The data is found to be in generally good agreement with the predictions for the two point frequency correlations and the frequency interval for successive repetitions of impedance matrix elements values.
22 Pages, 8 Figures. Submitted to Acta Physica Polonica A
References in corpus (41)
- The Statistical Theory of Quantum Dots
- Random Matrices and Chaos in Nuclear Physics
- Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions
- Experimental simulation of quantum graphs by microwave networks
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Universal Impedance Fluctuations in Wave Chaotic Systems
- Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
- Quantum Chaotic Scattering in Microwave Resonators
- Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
- Universal Statistics of the Scattering Coefficient of Chaotic Microwave Cavities
- Distribution of reflection coefficients in absorbing chaotic microwave cavities
- Statistics of Impedance and Scattering Matrices in Chaotic Microwave Cavities: Single Channel Case
- Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption
- Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
- Statistics of Impedance and Scattering Matrices of Chaotic Microwave Cavities with Multiple Ports
- Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers
- Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances
- In-situ Broadband Cryogenic Calibration for Two-port Superconducting Microwave Resonators
- Distribution of Scattering Matrix Elements in Quantum Chaotic Scattering
- The effect of short ray trajectories on the scattering statistics of wave chaotic systems
- Experimental Examination of the Effect of Short Ray Trajectories in Two-port Wave-Chaotic Scattering Systems
- Experimental Test of Universal Conductance Fluctuations by means of Wave-Chaotic Microwave Cavities
- Universal and non-universal properties of wave chaotic scattering systems
- A first-principles model of time-dependent variations in transmission through a fluctuating scattering environment
- Impedance and Scattering Variance Ratios of Complicated Wave Scattering Systems in the Low Loss Regime
- Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
- Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
- Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
- Experimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics
- How T-invariance violation leads to an enhanced backscattering with increasing openness of a wave-chaotic system
- Novel Topology and Manipulation of Scattering Singularities in Complex non-Hermitian Systems
- A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures
- Implementing Non-Universal Features with a Random Matrix Theory Approach: Application to Space-to-Configuration Multiplexing
- Control of the Scattering Properties of Complex Systems By Means of Tunable Metasurfaces
- Cross-Section Fluctuations in Chaotic Scattering Systems
- Correlation functions and correlation widths in Quantum-Chaotic Scattering for mesoscopic systems and nuclei
- Universal S-matrix correlations for complex scattering of many-body wavepackets: theory, simulation and experiment
- Topological Singularities in Metasurface Scattering Matrices: From Nodal Lines to Exceptional Lines
- Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
- Time Domain Generalization of the Random Coupling Model and Experimental Verification in a Complex Scattering System
- Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities