Abstract
We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard microwave cavities are discussed in terms of universal predictions from random matrix theory, as well as periodic orbit contributions which manifest as “scars” in eigenfunctions. The semiclassical and classical Ruelle zeta-functions lead to quantum and classical resonances, both of which are observed in microwave experiments on n-disk hyperbolic billiards.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
S. Smale, Bull. Amer. Math. Soc. 73:747 (1967).
Ya. Sinai, Russian Math. Surveys 25:137 (1970).
M. Wojtkowski, Comm. Math. Phys. 105:391 (1986).
L. A. Bunimovich, Comm. Math. Phys. 65:295 (1979).
D. Ruelle, Phys. Rev. Lett. 56:405 (1986); J. Stat. Phys. 44:481 (1986).
M. Pollicott, Ann. Math. 131:331 (1990).
S. Sridhar, Phys. Rev. Lett. 67:785 (1991).
A. Kudrolli, S. Sridhar, A. Pandey, and R. Ramaswamy, Phys. Rev. E 49:R11 (1994).
P. Pradhan and S. Sridhar, Phys. Rev. Lett. 85:2360 (1995).
A. Kudrolli, V. Kidambi, and S. Sridhar, Phys. Rev. Lett. 75:822 (1995).
W. Lu, M. Rose, K. Pance, and S. Sridhar, Phys. Rev. Lett. 82:5233 (1999); W. Lu, L. Viola, K. Pance, M. Rose, and S. Sridhar, Phys. Rev. E 61:3652 (2000).
K. Pance, W. Lu, and S. Sridhar, Phys. Rev. Lett. 85:2737 (2000); W. T. Lu, K. Pance, P. Pradhan, and S. Sridhar, Phys. Scrip. T90:238 (2001).
S. Sridhar and A. Kudrolli, Phys. Rev. Lett. 72:2175 (1994).
T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299:189 (1998).
H.-J. Stockmann, Quantum Chaos: An Introduction (Cambridge University Press, 1999).
S. Sridhar, D. Hogenboom, and B. A. Willemsen, J. Stat. Phys. 68:239 (1992).
E. J. Heller, Phys. Rev. Lett. 53:1515 (1984).
P. Gaspard and S. A. Rice, J. Chem. Phys. 91:2225, 2242, 2255 (1989).
M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, 1990).
L.-S. Young, Notices of the AMS 45:1318 (1998); Ann. Math. 147:585 (1998).
P. Cvitanović and B. Eckhardt, J. Phys. A 24:L237 (1991).
P. Gaspard, D. Alonso, T. Okuda, and K. Nakamura, Phys. Rev. E 50:2591 (1994).
P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, and G. Vattay, Classical and Quantum Chaos, www.nbi.dk/ChaosBook/ (Niels Bohr Institute, Copenhagen, 2001).
P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, 1998).
P. Cvitanović and B. Eckhardt, Phys. Rev. Lett. 63:823 (1989).
C. Manderfeld, J. Weber, and F. Haake, J. Phys. A 34:9893 (2001).
O. Bohigas, P. Leboeuf, and M. J. Sanchez, Found. Phys. 31:489 (2001).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sridhar, S., Lu, W.T. Sinai Billiards, Ruelle Zeta-functions and Ruelle Resonances: Microwave Experiments. Journal of Statistical Physics 108, 755–765 (2002). https://doi.org/10.1023/A:1019714808787
Issue Date:
DOI: https://doi.org/10.1023/A:1019714808787