Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems
arXiv:cond-mat/0512131 · doi:10.1103/PhysRevE.74.036213
Abstract
Statistical fluctuations in the eigenvalues of the scattering, impedance and admittance matrices of 2-Port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity. We remove the direct processes introduced by the non-ideally coupled driving ports through a matrix-normalization process that involves the radiation-impedance matrix of the two driving ports. We find good agreement between the experimentally obtained marginal probability density functions (PDFs) of the eigenvalues of the normalized impedance, admittance and scattering matrix and those from Random Matrix Theory (RMT). We also experimentally study the evolution of the joint PDF of the eigenphases of the normalized scattering matrix as a function of loss. Experimental agreement with the theory by Brouwer and Beenakker for the joint PDF of the magnitude of the eigenvalues of the normalized scattering matrix is also shown.
12 Pages, 8 Figures, All figures in Color, Submitted to Phys. Rev. E. Updated with Revisions (July 10th, 2006)
References in corpus (21)
- Random-Matrix Theory of Quantum Transport
- The Statistical Theory of Quantum Dots
- Voltage-probe and imaginary potential models for dephasing in a chaotic quantum dot
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NON-IDEAL LEADS
- Universal Impedance Fluctuations in Wave Chaotic Systems
- How Phase-Breaking Affects Quantum Transport Through Chaotic Cavities
- Distributions of the Conductance and its Parametric Derivatives in Quantum Dots
- Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
- 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
- Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem
- Statistics of Impedance and Scattering Matrices of Chaotic Microwave Cavities with Multiple Ports
- Characterization of Fluctuations of Impedance and Scattering Matrices in Wave Chaotic Scattering
- Universal transport properties of open microwave cavities with and without time-reversal symmetry
- Complete S-matrix in a microwave cavity at room temperature
- Global versus local billiard level dynamics: The limits of universality
- Measurement of Wave Chaotic Eigenfunctions in the Time-Reversal Symmetry-Breaking Crossover Regime
- Mesoscopic conductance fluctuations in dirty quantum dots with single channel leads
- Statistical wave scattering through classically chaotic cavities in the presence of surface absorption
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