

Affiliations: 

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, twodimensional 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 "bowtie" 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 (S_{12}) measurements, and the eigenfunctions are imaged by means of a scanned perturbation technique.
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 apriori 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 nonuniversal 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 timereversal properties of the wave equation. Our initial work investigates basic properties of a simple onerecording channel timereversal mirror for electromagnetic waves. We have also developed a new sensor paradigm that exploits timereversal 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 Center of Excellence 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 TimeReversed Wave Propagation Papers: (All papers can be downloaded from the full publication list) 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 2Port 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 WaveChaotic 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 TimeReversed Electromagnetics: High Frequency OneRecordingChannel 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 JenHao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, “Universal and nonuniversal properties of wave chaotic scattering systems,” Phys. Rev. E 81, 025201(R) (2010). pdf JenHao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, “Experimental Examination of the Effect of Short Ray Trajectories in Twoport WaveChaotic Scattering Systems,” Phys. Rev. E 82, 041114 (2010). pdf G. Gradoni, JenHao 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. 202207. 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. 220225. 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 WaveChaotic Approach,” IEEE Trans. Electromag. Compat. 54, 758771 (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 JenHao Yeh, Thomas M. Antonsen, Edward Ott, Steven M. Anlage, “Firstprinciples model of timedependent variations in transmission through a fluctuating scattering environment,” Phys. Rev. E (Rapid Communications) 85, 015202 (2012). pdf JenHao Yeh, Edward Ott, Thomas M. Antonsen, Steven M. Anlage, “Fading Statistics in Communications  a Random Matrix Approach,” Acta Physica Polonica A, 120, A85 (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. JenHao Yeh and Steven Analge, "Insitu Broadband Cryogenic Calibration for Twoport Superconducting Microwave Resonators," Rev. Sci. Instrum. 84, 034706 (2013). pdf Gabriele Gradoni, JenHao 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, 606621 (2014). pdf MingJer 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 JenHao 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 G. Gradoni, Xiaoming Chen, T. M. Antonsen, Steven M. Anlage, Edward Ott, “Random coupling model for wireless communication channels,” 2014 International Symposium on Electromagnetic Compatibility (EMC Europe), pp. 878882 (2014). pdf Zachary B. Drikas, Jesus Gil Gil, Hai V. Tran, Sun K. Hong, Tim D. Andreadis, JenHao Yeh, Biniyam T. Taddese and Steven M. Anlage, “Application of the Random Coupling Model to Electromagnetic Statistics in Complex Enclosures,” IEEE Trans. Electromag. Compat. 56, 14801487 (2014). pdf Gabriele Gradoni, Thomas M. Antonsen, Steven M. Anlage, and Edward Ott, “A Statistical Model for the Excitation of Cavities Through Apertures,” IEEE Trans. Electromag. Compat., 57 (5) 10491061 (2015). pdf 

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