Abstract
We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the quantum dynamics takes place in a finite dimensional Hilbert space. We find a distinction between regular and irregular behavior for times exceeding the quantum mechanical quasiperiod at which classical behavior, whether chaotic or regular, has died out in quantum means. The degree of level repulsion depends on whether or not the top is endowed with a generalized time reversal invariance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
McDonald, S., Kaufman, A.N.: Phys. Rev. Lett.42, 1189 (1979)
Casati, G., Chirikov, B.V., Izrailev, F.M., Ford, J.: Stochastic behavior in classical and quantum hamiltonian systems. In: Lecture Notes in Physics. Casati, G., Ford, J. (eds.), Vol. 93, p. 334. Berlin, Heidelberg, New York: Springer 1979
Casati, G., Mantica, G., Guarneri, I.: In: Chaotic behavior in quantum systems. Casati, G. (ed.), p. 113. New York: Plenum Press 1985
Izrailev, F.M.: Quasi-energy level spacing distribution for quantum systems stochastic in the classical limit. (in Russian), Inst. of Nuclear Physics, Novosibirsk, Preprint No. 84-63 (1984)
Izrailev, F.M.: Phys. Rev. Lett.56, 541 (1986)
Hogg, T., Huberman, B.A.: Phys. Rev. Lett.48, 711 (1982)
Bohigas, O., Giannoni, M.J., Schmit, C.: Phys. Rev. Lett.52, 1 (1984)
Haller, E., Köppel, H., Cederbaum, L.S.: Phys. Rev. Lett.52, 1165 (1984)
Seligman, T.H., Verbaarscot, J.J.M.: Phys. Lett.108A, 183 (1985)
Berry, M.V., Tabor, M.: Proc. R. Soc. London Ser. A356, 375 (1977)
Haake, F., Kuś, M., Mostowski, J., Scharf, R.: In: Coherence, cooperation and fluctuations. Haake, F., Narducci, L., Walls, D. (eds.), p. 220. Cambridge: Cambridge University Press 1986
Frahm, H., Mikeska, H.J.: Z. Phys. B—Condensed Matter60, 117 (1985)
Arecchi, F.T., Courtens, E., Gilmore, R., Thomas, H.: Phys. Rev. A6, 2211 (1972)
Glauber, R.J., Haake, F.: Phys. Rev. A13, 357 (1976)
Waldner, F., Barberis, D.R., Yamazaki, H.: Phys. Rev. A31, 420 (1985)
Reynaud, S.: Private Communication
McKay, R.S.: Renormalization in area preserving maps. Ph.D. thesis, Princeton 1982
DeVogelaere, R.: In: Contributions to the theory of nonlinear oscillations. Lefschetz, S. (ed.), Vol. IV, p. 53. Princeton: Princeton University Press 1958
Lichtenberg, A.J., Lieberman, M.A.: Regular and stochastic motion. Berlin, Heidelberg, New York: Springer 1982
Eberly, J.H., Narozhny, N.B., Sanchez-Mondragon, J.J.: Phys. Rev. Lett.44, 1323 (1980)
Graham, R., Höhnerbach, M.: in: Proceedings of the Topical Meeting on Instabilities and Dynamics of Lasers. Rochester 1985 (to be published)
Feingold, M., Fishman, S., Grempel, D.R., Prange, R.E.: Phys. Rev. B31, 6852 (1985)
Pechukas, P.: Phys. Rev. Lett.51, 943 (1983)
Yukawa, T.: Phys. Rev. Lett.54, 1883 (1985)
Dyson, F.J.: J. Math. Phys.3, 140, 157, 166 (1962)
Porter, C.E.: In: Statistical theories of spectra. Porter, C.E. (ed.), p. 3. New York: Academic Press 1965
Robnik, M., Berry, M.V.: J. Phys. A19, 669 (1986)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Haake, F., Kuś, M. & Scharf, R. Classical and quantum chaos for a kicked top. Z. Physik B - Condensed Matter 65, 381–395 (1987). https://doi.org/10.1007/BF01303727
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01303727