Abstract
This review is concerned with dynamical consequences of the quantization of systems with classically chaotic dynamics. It is argued that such systems display an instability in the classical limit. The standard map is used as a prototype. Besides a discussion of the phenomenon of localization in action space due to quantum interferences, we consider in particular the effects of repeated measurements and of dissipation which tend both to reduce or destroy localization phenomena and trigger the instability otherwise only encountered when taking the classical limit.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
O. Bohigas, M.J. Giannoni, C. Schmit, Phys. Rev. Lett. 52, 1 (1984);
E. Haller, H. Koppel, L.S. Cederbaum, Phys. Rev. Lett. 52,1165 (1984).
B.V. Chirikov, Preprint no. 267, Inst. Nucl. Phys., Novosibirsk (1969); Phys. Rep. 52, 263 (1979).
A.J. Lichtenberg, M.A. Lieberman, Regular and Stochastic Motion, Springer, Berlin 1983.
G. Casati, B.V. Chirikov, F.M. Izrailev, J. Ford, in Lecture Notes in Physics vol. 93, p. 334, Springer, Berlin 1979.
B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Sov. Sci. Rev. C2, 209 (1981).
S. Fishman, D.R. Grempel, R.E. Prange, Phys. Rev. Lett. 49, 509 (1982);
S. Fishman, D.R. Grempel, R.E. Prange, Phys. Rev. A29, 1639 (1984).
D.L. Shepelyansky, Phys. Rev. Lett. 56, 677 (1986).
T. Dittrich, R. Graham, Z. Physik B62, 515 (1986).
T. Dittrich, R. Graham, Europhys. Lett. 4, 263 (1987).
T. Dittrich, R. Graham, in Chaos and Related Nonlinear Phenomena; Where Do We Go From Here?, ed. I. Procaccia, Plenum, New York 1988.
R.S. MacKay, J.D. Meiss, I.C. Percival, Physica D13, 55 (1984).
A.B. Rechester, R.B. White, Phys. Rev. Lett. 44, 1586 (1980).
G. Casati, J. Ford, I. Guarneri, F. Vivaldi, Phys. Rev. A34, 1413 (1986).
F.M. Izrailev, D.L. Shepelyansky, Teor. Mat. Fiz. 43, 417 (1980).
G. Floquet, Ann. de l’Ecole Norm. Sup. 12, 47 (1983).
E.V. Shuryak, Zh. Eksp. Teor. Fiz. 71, 2039 (1976). (Sov. Phys. JETP 44, 1070 (1976)).
A.O. Caldeira, A.J. Leggett, Phys. Rev. Lett. 46, 211 (1981);
A.O. Caldeira, A.J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983);
A.O. Caldeira, A.J. Leggett, Ann. Phys. (N.Y.) 153, 445 (1984).
R. Graham, Europhys. Lett. 3, 259 (1987).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Dittrich, T., Graham, R. (1989). Quantum Chaos. In: Tirapegui, E., Villarroel, D. (eds) Instabilities and Nonequilibrium Structures II. Mathematics and Its Applications, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2305-8_11
Download citation
DOI: https://doi.org/10.1007/978-94-009-2305-8_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7535-0
Online ISBN: 978-94-009-2305-8
eBook Packages: Springer Book Archive