Abstract
We present a study of a series of eigenstates occurring in the wedge billiard which may be quantized about tori by sejiclassical adiabatic quantization, even though the underlying classical system exhibits hard chaos and strictly possesses no tori. We also show that adiabatic eigenstates should be common in many chaotic systems, especially among the lower eigenstates, and present a heuristic argument as to why this should be so.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Dahlqvist,J. Phys. A 25:6265 (1992).
Y. Y. Bai, B. Hose, K. Stefanski, and H. S. Taylor,Phys. Rev. A 31:2821 (1985).
M. Sieber and F. Steiner,Physica D 44:248 (1990).
S. W. McDonald, Ph.D. Thesis, University of California (Berkeley) (1983).
B. Eckhardt, G. Hose, and E. Pollak,Phys. Rev. A 39:3776 (1989).
P. A. Dando, T. S. Montiero, W. Jans, and W. Schwiezer,Prog. Theor. Phys. Suppl. 116:403 (1994).
W. Jans, T. S. Montiero, W. Schweizer, and P. A. Dando,J. Phys. A 26:3187 (1993).
I. C. Percival and D. Richards,Introduction to Dynamics (Cambridge University Press, Cambridge, 1982).
L. I. Schiff,Quantum Mechanics, 3rd ed. (McGraw-Hill, New York, 1968); S. K. Knudson and D. W. Noid,J. Chem. Ed. 66:133 (1989).
T. Szeredi and D. A. Goodings,Phys. Res. E.48:3518 (1993); N. D. Whelan, D. A. Goodings, and J. K. Cannizzo,Phys. Rev. A 42:742 (1990); N. I. Chernov,Physica D 53:233 (1991); M. P. Wojtkowski,Commun. Math. Phys. 126:507 (1990); P. H. Richter, H. J. Scholz, and A. Wittek,Nonlinearity 3:45 (1990); H. E. Lehtihet and B. N. Miller,Physica D 21:93 (1986).
T. Szeredi, J. H. Lefebre, and D. A. Goodings,Nonlinearity 7:1463 (1994); T. Szeredi and D. A. Goodings,Phys. Rev. E 48:3529 (1993); C. Rouvinez and U. Smilansky,J. Phys. A 28:77 (1995); A. Wittek, Die Quantenmechanik eines nichtintegrablen systems; klassisch chaotisches billiard in gravitationsfeld, Ph.D. Thesis, Bremen (1991).
M. Kac,Am. Math. Monthly 73, 1 (1966).
M. V. Berry,Eur. J. Phys. 2:91 (1981).
E. P. Wigner,Phys. Rev. 40:749 (1932).
M. V. Berry, Semiclassical mechanics of regular and irregular motion, inLes Houches, Session XXXVI, Chaotic Behavior of Deterministic Systems (North-Holland, Amsterdam, 1983).
M. V. Berry,Proc. Soc. A 287:237 (1977).
M. C. Gutzwiller,Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Szeredi, T. Hard chaos and adiabatic quantization: The wedge billiard. J Stat Phys 83, 259–274 (1996). https://doi.org/10.1007/BF02183649
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02183649