Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems

Details Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems

2005-12-06

arxiv.org/abs/cond-mat/0512131v4

Phys. Rev. E 74, 036213 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 Pages, 8 Figures, All figures in Color, Submitted to Phys. Rev. E. Updated with Revisions (July 10th, 2006)

Scientific paper

10.1103/PhysRevE.74.036213

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.

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