Quantum Chaos is the study of the quantum mechanics of classically chaotic systems. The field is currently a very active area of research. Our main thrust is to explore, via electromagnetic experiments, the manifestations of classical chaos in wave mechanics.

Our research program has led to several noteworthy observations listed below:

  • Experimental “proof” of a mathematical theorem on “Not Hearing the Shape of Drums”. Click here to see cover story in Science News.
  • Direct experimental observation of scars in quantum eigenfunctions of microwave cavities. Phys. Rev. Lett. , 67, 785 (1991)
  • Experimental observation of localized wavefunctions in disordered billiards, and deviations from the Porter-Thomas distribution due to localization in disordered billiards. These were the first experiments to be performed on disordered billiards. Phys. Rev. Lett., 75, 822 (1995)
  • First experimental observation of quantum fingerprints of classical Ruelle-Pollicott resonances. Phys. Rev. Lett., 85, 2360 (2000), Nobel Symposium on “Quantum Chaos Y2K”
  • Experimental studies of correlations of chaotic and disordered eigenfunctions and comparison with supersymmetry nonlinear sigma models. Phys. Rev. Lett., 85, 2360 (2000)
  • Tunneling Proximity Resonances: Experimental observation using dielectric resonators Phys. Lett. A, 268 (4-6), 399 (2000)
  • Precision tests of universal aspects of quantum spectra, observation of a “correlation hole”, and tests of applicability of Random Matrix Theories to microwave cavities. Phys. Rev. E. (Rapid Comm.), 49, R11 (1994)
  • Observation of Porter-Thomas distribution and fluctuations in eigenfunctions of chaotic billiards. Phys. Rev. Lett., 75, 822 (1995)
  • Observation of quantum resonances, universal properties, and comparison with semiclassical theories of the n-disk system. Phys. Rev. Lett., 82, 5233 (1999), Phys. Rev. E, 61, 3652 (2000)

It is evident that the experiments are able to explore a remarkable range of issues in Quantum Chaos, including tests of fundamental theories and different classical limits. The microwave experiments have yielded entirely new insights and perspectives concerning the quantum-classical correspondence. The reasons for this success are the ability to study well-defined geometries where the classical dynamics is clearly known, and the precision and flexibility of the experiments. The experiments have led to tests of key theoretical ideas while at the same time raising entirely new questions and motivating theorists in new directions.

Our work in this area is currently funded by National Science Foundation (Division of Atomic, Molecular and Optical Physics).

Related Posts

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Wavefunctions in Chaotic and Disordered Geometries

The Sinai-Stadium billiard is a prototype example of chaotic geometries. Representative eigenfunctions of this geometry are shown here. The influence of the classical dynamical structures such as periodic orbits can be seen in some of the wavefunctions. The Sinai-Stadium was designed to have no non-isolated periodic orbits, which leads to deviation from universality.

Related Publications

Lu, WT; Zeng, Weiqiao; Sridhar, S

Duality between quantum and classical dynamics for integrable billiards Journal Article

In: Physical Review E, 73 (4), pp. 046201, 2006.

Abstract | Tags: Quantum Chaos

Lu, WT; Sridhar, S

Long range correlations among the eigenvalues of polygonal billiards and Riemann zeros Journal Article

In: APS, 2004 , pp. D19–004, 2004.

Abstract | Tags: Quantum Chaos

Lu, WT; Sridhar, S

Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality Journal Article

In: arXiv preprint nlin/0405058, 2004.

Abstract | Tags: Quantum Chaos

Lu, WT; Sokoloff, JB; Sridhar, S

Classical physics, including nonlinear media and photonic materials-Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative Journal Article

In: Physical Review-Section E-Statistical Nonlinear and Soft Matter Physics, 69 (2), pp. 26604–26604, 2004.

Tags: Quantum Chaos

Wen-tao, Lu T; Sridhar, Srinivas; Zworski, Maciej

Fractal Weyl laws for chaotic open systems Journal Article

In: 2003.

Abstract | Tags: Quantum Chaos

Pradhan, Prabhakar; Lu, Wentao T; Sridhar, S

Statistics of the Eigenfunctions of Chaotic and Disordered Quantum Systems: A Disordered Tight Binding Model Calculation Inproceedings

In: APS Meeting Abstracts, 2003.

Abstract | Tags: Quantum Chaos

Lu, WT; Sridhar, Srinivas; Zworski, Maciej

Fractal Weyl laws for chaotic open systems Journal Article

In: Physical review letters, 91 (15), pp. 154101, 2003.

Abstract | Tags: Quantum Chaos

Sato, Daisuke; Lu, Wentao; Pradhan, Prabhakar; Sridhar, Srinivas

Spectral statistics of microwave disordered billiards Inproceedings

In: APS Meeting Abstracts, 2003.

Abstract | Tags: Quantum Chaos

Dhar, Abhishek; Rao, Madhusudhana D; Sridhar, S; others,

Isospectrality in chaotic billiards Journal Article

In: Physical Review E, 68 (2), pp. 026208, 2003.

Abstract | Tags: Quantum Chaos

Sridhar, S; Lu, WT

Sinai billiards, Ruelle zeta-functions and Ruelle resonances: microwave experiments Journal Article

In: Journal of statistical physics, 108 (5-6), pp. 755–765, 2002.

Abstract | Tags: Quantum Chaos

Pradhan, Prabhakar; Sridhar, S

From chaos to disorder: Statistics of the eigenfunctions of microwave cavities Journal Article

In: Pramana, 58 (2), pp. 333–341, 2002.

Abstract | Tags: Quantum Chaos

Sridhar, S; Lu, WT

Sinai billiards, Ruelle zeta-functions and Ruelle resonances: microwave experiments. e-print Journal Article

In: 2002.

Abstract | Tags: Quantum Chaos

Sinai, Ya G; Young, Lai-Sang; Sridhar, S; Lu, WT; van Beijeren, Henk; Dorfman, JR; Jakšic, V; Pillet, CA; Gallavotti, G; Lebowitz, JL; others,

Some Ill-Formulated Problems on Regular and Messy Behavior in Statis-tical Mechanics and Smooth Dynamics for Which I Would Like the Advice of Yasha Sinai David Ruelle What, in My Opinion, David Ruelle Should Do in the Coming Years Journal Article

In: Journal of Statistical Physics, 108 (3/4), 2002.

Tags: Quantum Chaos

Lu, WT; Sridhar, S; others,

Spectra and wave functions of open chaotic billiards Inproceedings

In: APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts, 2002.

Abstract | Tags: Quantum Chaos

Sridhar, Srinivas

Quantum Chaos in Microwave Billiards Inproceedings

In: APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts, 2002.

Abstract | Tags: Quantum Chaos

Lu, Wentao T; Prance, Kristi; Pradhan, Prabhakar; Sridhar, S

Quantum correlations and classical resonances in an open chaotic system Journal Article

In: Physica Scripta, 2001 (T90), pp. 238, 2001.

Abstract | Tags: Quantum Chaos

Sridhar, S

Quantum resonances and decay of a fractal repeller observed using microwaves Inproceedings

In: APS Meeting Abstracts, 2000.

Abstract | Tags: Quantum Chaos

Sridhar, S

Quantum chaos, localization and tunnelling: microwave experiments on model geometries Journal Article

In: Philosophical Magazine B, 80 (12), pp. 2129–2141, 2000.

Abstract | Tags: Quantum Chaos

Pance, Kristi; Lu, Wentao; Sridhar, S

Quantum fingerprints of classical ruelle-pollicott resonances Journal Article

In: Physical review letters, 85 (13), pp. 2737, 2000.

Abstract | Tags: Quantum Chaos

Pradhan, Prabhakar; Sridhar, S

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities Journal Article

In: Physical review letters, 85 (11), pp. 2360, 2000.

Abstract | Tags: Quantum Chaos

Pradhan, Prabhakar; Pance, Kristi; Rose, Michael; Sridhar, S

From Localization to Chaos in experimental eigenfunctions of disordered microwave cavities Inproceedings

In: APS Meeting Abstracts, 2000.

Abstract | Tags: Quantum Chaos

Lu, Wentao; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S

Microwave study of quantum n-disk scattering Journal Article

In: Physical Review E, 61 (4), pp. 3652, 2000.

Abstract | Tags: Quantum Chaos

Pance, Kristi; Viola, Lorenza; Sridhar, S

Tunneling proximity resonances: interplay between symmetry and dissipation Journal Article

In: Physics Letters A, 268 (4-6), pp. 399–405, 2000.

Abstract | Tags: Quantum Chaos

Lu, Wentao; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S

Erratum: Microwave study of quantum n-disk scattering [Phys. Rev. E 61, 3652 (2000)] Journal Article

In: Physical Review E, 62 (3), pp. 4478, 2000.

Abstract | Tags: Quantum Chaos

Lu, Wentao; Rose, M; Pance, K; Sridhar, S

Quantum resonances and decay of a chaotic fractal repeller observed using microwaves Journal Article

In: Physical review letters, 82 (26), pp. 5233, 1999.

Abstract | Tags: Quantum Chaos

Sridhar, S

Wave Chaos and Localization in Closed Billiards and Open Scattering Systems: Microwave Experiments Inproceedings

In: APS March Meeting Abstracts, 1998.

Abstract | Tags: Quantum Chaos

Kudrolli, A; Sridhar, S

Experiments on quantum chaos using microwave cavities: Results for the pseudo-integrable L-billiard Journal Article

In: Pramana, 48 (2), pp. 459–467, 1997.

Abstract | Tags: Quantum Chaos

Jacobs, T; Willemsen, Balam A; Sridhar, S

Quantitative analysis of nonlinear microwave surface impedance from non-Lorentzian resonances of high Q resonators Journal Article

In: Review of scientific instruments, 67 (10), pp. 3757–3758, 1996.

Tags: Quantum Chaos

Kudrolli, A; Sridhar, S

Comment on “Gaussian Orthogonal Ensemble Statistics in a Microwave Stadium Billiard with Chaotic Dynamics: Porter-Thomas Distribution and Algebraic Decay of Time Correlations” Journal Article

In: Physical review letters, 76 (16), pp. 3036, 1996.

Abstract | Tags: Quantum Chaos

Kudrolli, A; Kidambi, V; Sridhar, S

Experimental studies of chaos and localization in quantum wave functions Journal Article

In: Physical review letters, 75 (5), pp. 822, 1995.

Abstract | Tags: Quantum Chaos

Prigodin, VN; Taniguchi, Nobuhiko; Kudrolli, A; Kidambi, V; Sridhar, S

Spatial correlation in quantum chaotic systems with time-reversal symmetry: Theory and experiment Journal Article

In: Physical review letters, 75 (12), pp. 2392, 1995.

Abstract | Tags: Quantum Chaos

Kudrolli, A; Sridhar, S

QUANTUM CHAOS EXPERIMENTS USING MICROWAVE CAVITIES Inproceedings

In: Proceedings Of The 2nd Experimental Chaos Conference, pp. 184, World Scientific 1995.

Abstract | Tags: Quantum Chaos

Sridhar, S

Cavities of Chaos Journal Article

In: SCIENCE NEWS-WASHINGTON-, 147 , pp. 264–264, 1995.

Tags: Quantum Chaos

Kudrolli, A; Sridhar, S; Pandey, Akhilesh; Ramaswamy, Ramakrishna

Signatures of chaos in quantum billiards: Microwave experiments Journal Article

In: Physical Review E, 49 (1), pp. R11, 1994.

Abstract | Tags: Quantum Chaos

Sridhar, S

Quantum Dynamics of Chaotic Systems Journal Article

In: 1993.

Tags: Quantum Chaos

Sridhar, S; Hogenboom, D; Kudrolli, A

Exper-imental eigenvalue spectra of “rough” and multiplyconnected billiards,” Journal Article

In: Quantum Dynamics of Chaotic Systems, eds. Yuan, JM, Feng, DH & Zaslavsky, GM (Gordon and Breach, Amsterdam), pp. 297–304, 1993.

Abstract | Tags: Quantum Chaos

Sridhar, S; Heller, EJ

Physical and numerical experiments on the wave mechanics of classically chaotic systems Journal Article

In: Physical Review A, 46 (4), pp. R1728, 1992.

Abstract | Tags: Quantum Chaos

Sridhar, S; Hogenboom, DO; Willemsen, Balam A

Microwave experiments on chaotic billiards Journal Article

In: Journal of statistical physics, 68 (1-2), pp. 239–258, 1992.

Abstract | Tags: Quantum Chaos

Sridhar, S; Parimi, PV; Lu, WT; Vodo, P; Derov, John S; Hanscom, AFRL; Bedford, MA

Negative Refraction and Imaging in Photonic Crystals Journal Article

In: 0000.

Abstract | Tags: Quantum Chaos

Harika, K; Swetha, BV; Renuka, B; Rao, Lakshman D; Sridhar, S

Analysis of Different Multiplication Algorithms & FPGA Implementation Journal Article

In: IOSR Journal of VLSI and Signal Processing (IOSR-JVSP), 4 (2), pp. 29–35, 0000.

Tags: Quantum Chaos