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There is great interest in the quantum/wave properties of systems that show chaos in the classical (short wavelength, or ray) limit. These wave chaotic systems appear in many contexts: nuclear physics, acoustics, two-dimensional quantum dots, and electromagnetic enclosures. Random matrix theory has been widely used to understand the universal properties of these systems through the statistical description of their eigenvalues, eigenfunctions, and scattering matrices.

We have developed a simple experiment to study the wave chaos properties of a microwave resonator that has the shape of a quarter "bow-tie" as shown in Fig. 1. The shape is such that the corresponding ray trajectories are chaotic and all periodic ray trajectories are unstable. The eigenvalue spectrum is determined using transmission (S₁₂) measurements, and the eigenfunctions are imaged by means of a scanned perturbation technique.

Fig. 1 Eigenmode image of the 1/4-bow-tie wave-chaotic resonator.

We have extended our understanding of quantum/wave chaotic systems by providing experimental evidence for the universality of the complex impedance and scattering matrices of such systems in accordance with the newly developed Random Coupling Model (RCM). The RCM is a stochastic model based upon the a-priori knowledge of the statistical properties of the chaotic eigenvalues and eigenfunctions of the system, and is capable of incorporating both the universal fluctuations in the impedance of such enclosures, as well as non-universal quantities that are specific to a given geometry and coupling mechanisms. The statistical properties of the impedance and scattering matrices can be related to transport properties of mesoscopic systems, for example.

We have taken this work in a new direction to investigate the role of chaos on time-reversal properties of the wave equation. Our initial work investigates basic properties of a simple one-recording channel time-reversal mirror for electromagnetic waves. Further work is in progress with both electromagnetic and acoustic time-reversal mirrors.

This work is done in collaboration with Profs. Ed Ott and Tom Antonsen of the University of Maryland and is supported by the ONR and USAF MURI and DURIP programs.

Prof. Anlage talk: "Experimental Investigation of Universal Fluctuations in Quantum/Wave Chaotic Scattering Systems"

Graduate student Sameer Hemmady has an overview of his research on quantum chaos in his own words. Sameer won the GSNP Student Speaker Award at the 2006 APS March Meeting.

Here is a link to the Random Coupling Model web site. Prof. Anlage APS March Meeting 2007 talk.

Papers: (All papers can be downloaded from the full publication list)
Sameer Hemmady, Xing Zheng, Edward Ott, Thomas M. Antonsen, and Steven M. Anlage, "Universal Impedance Fluctuations in Wave Chaotic Systems," Phys. Rev. Lett. 94, 014102 (2005). pdf

Sameer Hemmady, Xing Zheng, Thomas M. Antonsen, Edward Ott, and Steven M. Anlage, "Universal Statistics of the Scattering Coefficient of Chaotic Microwave Cavities," Phys. Rev. E 71, 056215 (2005). pdf

Xing Zheng, Thomas M. Antonsen Jr., Edward Ott, "Statistics of Impedance and Scattering Matrices in Chaotic Microwave Cavities: Single Channel Case," Electromagnetics 26, 3 (2006). pdf, formerly known as: cond-mat/0408327.

Xing Zheng, Thomas M. Antonsen Jr., Edward Ott, "Statistics of Impedance and Scattering Matrices of Chaotic Microwave Cavities with Multiple Ports," Electromagnetics 26, 37 (2006). pdf, formerly known as: cond-mat/0408317.

Xing Zheng, Sameer Hemmady, Thomas M. Antonsen Jr., Steven M. Anlage, and Edward Ott, "Characterization of Fluctuations of Impedance and Scattering Matrices in Wave Chaotic Scattering," Phys. Rev. E 73 , 046208 (2006). pdf.

S. Hemmady, X. Zheng, T.M. Antonsen, E. Ott, S.M. Anlage, "Universal Properties of 2-Port Scattering, Impedance and Admittance Matrices of Wave Chaotic Systems," Phys. Rev. E 74 , 036213 (2006). pdf cond-mat/0512131.

Sameer Hemmady, Xing Zheng, Thomas M. Antonsen Jr., Edward Ott and Steven M. Anlage, "Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities," Acta Physica Polonica A 109, 65 (2006). pdf nlin.CD/0506025.

Sameer Hemmady , James Hart , Xing Zheng, Thomas M. Antonsen Jr., Edward Ott, Steven M. Anlage, “ Experimental Test of Universal Conductance Fluctuations by means of Wave-Chaotic Microwave Cavities ,” Phys. Rev. B 74, 195326 (2006). pdf cond-mat/0606650 .

Steven M. Anlage, John Rodgers, Sameer Hemmady , James Hart , Thomas M. Antonsen, Edward Ott, “New Results in Chaotic Time-Reversed Electromagnetics: High Frequency One-Recording-Channel Time Reversal Mirror,” Acta Physica Polonica A 112, 569 (2007). pdf