Abstract
We discuss the quantum behaviour of systems which exhibit deterministic chaos in the classical limit. To this end we first examine the motion of a rotator under an external time-periodic δ-like perturbation. When the perturbation is strong enough, the classical motion is chaotic and diffusive while the quantum excitation remains strongly localized. A similar phenomenon takes place in the more physical problem of an hydrogen atom irradiated by a linearly polarized microwave field. In this latter case however, there exists a critical value of the microwave field intensity above which localization is destroyed and strong quantum excitation takes place. Numerical computations confirm the above theoretical predictions which also agree with the experimental results so far available.
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
For a clear and readable discussion see; Moser J., 1968, Memoirs Am. Math. Soc., No 81.
Chirikov B.V., 1979, Phys. Rep. 52 263.
Ford J, Walker G.H., 1969, Phys. Rev. 188 416.
Henon H., Heiles C, 1964, Astron. J. 69 73.
Ford J., Physics Today, April 1983.
Casati G., Guarneri I. and Vivaldi F., 1983, Phys. Rev. Lett. 51 727.
Percival I.C., 1973, J. Phys. B L. 229.
Proceedings of the II International Conference on Quantum Chaos, eds. T.H. Seligman and H. Nishioka, Lectures Notes, Physics Vol. 263.
G. Casati, B.V. Chirikov, F.M. Izrailev, J. Ford in “Stochastic Behaviour in Classical and Quantum Hamiltonian Systems”, Como, June 1977, Lectures Notes in Physics, Springer 93. (1979), 334.
G. Casati, J. Ford. I. Guarneri, F. Vivaldi Phys. Rev. A 34 (1986) 1413.
B.V. Chirikov, F.M. Izrailev, and D.L. Shepelyansky, (1981) Sov. Sci. Rev. Sec. C 2, 209.
G.P. Brivio, G. Casati, L. Perotti, I. Guarneri, Physica D 33 (1988) 51.
S. Fishman, D.R. Grempel and R.E. Prange, 1982, Phys. Rev. Lett. 12, 509.
S. Fishman, D.R. Grempel and R.E. Prange, 1984. Phys. Rev. A 22. 1639.
J.E. Bayfield, P.M. Koch, Phys. Rev. Lett. 33. (1974) 258.
J.C. Leopold, I.C. Percival, Phys. Rev. Lett. 41 (1978) 944.
G. Casati, I. Guarneri and D.L. Shepelyansky, Phys. Rev. A 36 (1987) 3501.
G. Casati, I. Guarneri, D. Shepelyansky, J.E.E.E. J. of Quantum Electr. 24 (1988) 1420.
G. Casati, B.V. Chirikov, I. Guarneri, D.L. Shepelyansky, Physics Report 154 (1987). 77.
G. Casati. B.V. Chirikov, D.L. Shepelyansky, Phys. Rev. Lett. 53 (1984) 2525.
R.V. Jensen, Phys. Rev. A 30 (1984) 386.
K. van Leeuwen, G. v. Oppen, S. Renwick, J. Bowlin, P. Koch, R. Jensen, O. Rath, D. Richards, G. Leopold, Phys. Rev. Lett. 55 (1985) 2231.
R. Blumel, U. Smilansky, Phys. Rev. Lett. 58 (1987) 2531.
P. Koch, private communication.
J.E. Bayfield, G. Casati, I. Guarneri, D.V. Sokol: “Localization of classically chaotic diffusion for Hydrogen Atoms in Microwave Fields”. Preprint.
E.J. Galvey, B.E. Sauer, L. doorman, P.M. Koch, D. Richards; “Microwave lonization of H Atoms; Breakdown of Classical Dynamics for High Frequencies”. Preprint.
R. Blumel, R. Graham, L. Sirko, U. Smilansky, H. Walther, K. Yamada; “Microwave excitation of Rydberg atoms in the presence of noise”, Preprint.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Casati, G. (1990). Chaos in Quantum Dynamics: An Overview. In: Nicolaides, C.A., Clark, C.W., Nayfeh, M.H. (eds) Atoms in Strong Fields. NATO ASI Series, vol 212. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9334-5_11
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9334-5_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9336-9
Online ISBN: 978-1-4757-9334-5
eBook Packages: Springer Book Archive