Localization in the quantum description of the periodically perturbed rotor

  • R. Blümel
  • S. Fishman
  • M. Griniasti
  • U. Smilansky
III. Time Dependent Systems
Part of the Lecture Notes in Physics book series (LNP, volume 263)


In this paper we present some recent results concerning localization phenomena in the quantum dynamics of the periodically perturbed rotor. We discuss the response of a planar rotor and of a diatomic molecule to a periodic train of smooth and finite field pulses and show that both cases correspond to an Anderson model on. a finite grid. The second topic is the study of the localization properties for the b-kicked rotor when the kicking strength is large, using the transfer matrix technique.


Lyapunov Exponent Transfer Matrix Diatomic Molecule Anderson Model Localization Length 
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  1. 1.
    B.V. Chirikov, Phys. Rep. 52, 263 (1979). B.V. Chirikov, F.M. Izrailev and D.L. Shepelyansky, Sov. Sci. Rev. Sect. C2, 209 (1981).Google Scholar
  2. 2.
    G.M. Zaslavsky, Phys. Rep. 80, 158 (1981).Google Scholar
  3. 3.
    G. Casati, B.V. Chirikov, F.M. Izrailev and J. Ford in: “Stochastic Behaviour in Classical and Hamiltonian Systems”, Lecture Notes in Physics, Vol. 93, p. 334 (Springer N.Y. (1979)).Google Scholar
  4. 4.
    F.M. Izrailev and D.L. Shepelyansky, Teor. Mat. Fiz. 43, 417 (1980), Theor. Math. Phys. 43, 553 (80) and Sov. Phys.-Dokl. 24, 996 (1979).Google Scholar
  5. 5.
    G. Casati and I. Guarneri, Commun. Math. Phys. 95, 121 (1984).Google Scholar
  6. 6.
    T. Hogg and B.A. Huberman, Phys. Rev. Lett. 48, 711 (1982) and Phys. Rev. A28, 22 (1983).Google Scholar
  7. 7.
    S. Fishman, D.R. Grempel and R.E. Prange, Phys. Rev. Lett. 49, 509 (1982), D.R. Grempel, R.E. Prange and S. Fishman, Phys. Rev. A29, 1639 (1984).Google Scholar
  8. 8.
    J.D. Hanson, E. Ott, and M. Antonsen, Phys. Rev. A29, 819 (1984).Google Scholar
  9. 9.
    S.J. Chang and K.J. Shi Phys. Rev. Lett. 55, 269 (1985).Google Scholar
  10. 10.
    R. Blümel, S. Fishman, and U. Smilansky, J. Chem. Phys. in Press (1986).Google Scholar
  11. 11.
    M. Feingold, S. Fishman, D.R. Grempel, and R.E. Prange, Phys. Rev. B31, 6852 (1985)Google Scholar
  12. 12.
    I. Shimada and T. Nagashima, Prog. Theor. Phys. 61, 1605 (1979).Google Scholar
  13. 13.
    This was established rigorously by F. Delyon, Y. Levy, and B. Souillard (to be published) using property (2).Google Scholar
  14. 14.
    This difference was observed in preliminary calculations by M.F. Feingold and S. Fishman, to be published.Google Scholar
  15. 15.
    D.L. Shepelyansky, Phys. Rev. Lett. 56, 677 (1986).Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • R. Blümel
    • 1
  • S. Fishman
    • 2
  • M. Griniasti
    • 2
  • U. Smilansky
    • 3
  1. 1.Technical UniversityMünchenGermany
  2. 2.Dept. of Physicsthe TechnionHaifaIsrael
  3. 3.Dept. of Nuclear Physicsthe Weizmann Inst.RehovotIsrael

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