|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.
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'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, 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.
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. 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
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
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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