Anlage Research Group

High Frequency Superconductivity, Microscopy, Nanophysics, and Chaos


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ECE Department

Quantum / Wave Chaos

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. We have also developed a new sensor paradigm that exploits time-reversal symmetry, spatial reciprocity, and chaotic scattering of waves to very sensitively measure small perturbations to a scattering environment (see our movie on YouTube). Biniyam Taddese won first place in the 2008 'Focusing Research on Entrepreneurial Empowerment' symposium for this work (see his Applied Physics Letter).

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 AFOSR MURI and DURIP programs.

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

Prof. Anlage's talk at the Experimental Chaos Conference, Lille, France.

Graduate student Sameer Hemmady has won the GSNP Student Speaker Award at the 2006 APS March Meeting.

Here is a link to the Random Coupling Model web site.

See the related page on Time-Reversed Wave Propagation

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.

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.

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.

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.

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.

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

James A. Hart, T. M. Antonse, E. Ott, "Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay," Phys. Rev. E 79 , 016208 (2009). pdf

James A. Hart, T. M. Antonsen, E. Ott, "The effect of short ray trajectories on the scattering statistics of wave chaotic systems," Phys. Rev. E 80, 041109 (2009). pdf

Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, Universal and non-universal properties of wave chaotic scattering systems, Phys. Rev. E 81, 025201(R) (2010). pdf

Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, “Experimental Examination of the Effect of Short Ray Trajectories in Two-port Wave-Chaotic Scattering Systems,” Phys. Rev. E 82, 041114 (2010). pdf 

G. Gradoni, Jen-Hao Yeh, T. M. Antonsen, S. M. Anlage, E. Ott, “Wave Chaotic Analysis of Weakly Coupled Reverberation Chambers,” proceedings of the 2011 IEEE International Symposium on Electromagnetic Compatibility, pp. 202-207. pdf

T. M. Antonsen, G. Gradoni, S. M. Anlage E. Ott, “Statistical Characterization of Complex Enclosures with Distributed Ports,” proceedings of the 2011 IEEE International Symposium on Electromagnetic Compatibility, pp. 220-225.          pdf 

Sameer Hemmady, Thomas M. Antonsen Jr., Edward Ott, Steven M. Anlage, “Statistical Prediction and Measurement of Induced Voltages on Components within Complicated Enclosures: A Wave-Chaotic Approach,” IEEE Trans. Electromag. Compat. 54, 758-771 (2012). pdf

L. M. Pecora, H. Lee, D.-H. Wu, T. Antonsen, M.-J. Lee, E. Ott, "Chaos regularization of quantum tunneling rates," Phys. Rev. E 83, 065201 (2011). pdf

Jen-Hao Yeh, Thomas M. Antonsen, Edward Ott, Steven M. Anlage, First-principles model of time-dependent variations in transmission through a fluctuating scattering environment, Phys. Rev. E (Rapid Communications) 85, 015202 (2012). pdf

Jen-Hao Yeh, Edward Ott, Thomas M. Antonsen, Steven M. Anlage, “Fading Statistics in Communications - a Random Matrix Approach,” Acta Physica Polonica A, 120, A-85 (2012). pdf.

Mark Herrera, Edward Ott, Thomas M. Antonsen, S. Fishman, “Echoes and revival echoes in systems of anharmonically confined atoms,” Phys. Rev. A 86, 023613 (2012). pdf.

Gabriele Gradoni, Thomas M. Antonsen, Jr., and Edward Ott, “Impedance and power fluctuations in linear chains of coupled wave chaotic cavities,” Phys. Rev. E 86, 046204 (2012). pdf.

Jen-Hao Yeh and Steven Analge, "In-situ Broadband Cryogenic Calibration for Two-port Superconducting Microwave Resonators," Rev. Sci. Instrum. 84, 034706 (2013).   pdf

Gabriele Gradoni, Jen-Hao Yeh, Bo Xiao, Thomas M. Antonsen, Steven M. Anlage, Edward Ott , “Predicting the statistics of wave transport through chaotic cavities by the Random Coupling Model: a review and recent progress,” Wave Motion 51, 606-621 (2014) pdf

Ming-Jer Lee, Thomas M. Antonsen, Edward Ott , "Statistical model of short wavelength transport through cavities with coexisting chaotic and regular ray trajectories," Phys. Rev. E 87, 062906 (2013).   pdf

G. Gradoni, T. M. Antonsen, S. M. Anlage, E. Ott, “Random coupling model for the radiation of irregular apertures,” Proceedings of 2013 URSI International Symposium on Electromagnetic Theory (EMTS), pages 272 – 275 (2013). pdf

Jen-Hao Yeh, Zachary Drikas, Jesus Gil Gil, Sun Hong, Biniyam T. Taddese, Edward Ott, Thomas M. Antonsen, Tim Andreadis, and Steven M. Anlage, “Impedance and Scattering Variance Ratios of Complicated Wave Scattering Systems in the Low Loss Regime,” Acta Phys. Polon. A 124, 1045 (2013). pdf

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