Driven Systems

  • L. E. Reichl
Part of the Institute for Nonlinear Science book series (INLS)


Until now, we have considered quantum systems with time independent Hamiltonians. In this chapter, we focus on the dynamics of quantum systems with time-periodic Hamiltonians as they undergo a transition from a regime in which they exhibit integrable-like behavior to a regime where they exhibit the manifestations of chaos. Time-periodic quantum systems, if they consist of a time-independent part driven by a time-periodic field, have in some cases proven to be amenable to analytic analysis. This is one of the reasons why they have received so much attention in recent years.


Drive System Stable Manifold Primary Resonance Microwave Field Schrodinger Equation 
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  1. Arfken, G. (1985): Mathematical Methods for Physicists (Academic Press, Orlando).Google Scholar
  2. Bardsley, J.N. and Sundaram, B. (1985): Phys. Rev. A32 689.ADSCrossRefGoogle Scholar
  3. Bayfield, J.E. and Koch, P.M. (1974): Phys. Rev. Lett. 33 258.ADSCrossRefGoogle Scholar
  4. Bayfield, J.E. and Pinnaduwage, L.A. (1985): Phys. Rev. Lett. 54 313.ADSCrossRefGoogle Scholar
  5. Bayfield, J.E. and Sokol, D.W. (1988): Phys. Rev. Lett. 61 2007.ADSCrossRefGoogle Scholar
  6. Berman, G.P. and Zaslavskii, G.M. (1977): Phys. Lett. A61 295.CrossRefGoogle Scholar
  7. Berman, G.P., Zaslavskii, G.M., and Kolovsky, A.R. (1982): Phys. Lett. A87 152.CrossRefGoogle Scholar
  8. Berman, G.P. and Kolovsky, A.R. (1983a): Physica D8 117.MathSciNetGoogle Scholar
  9. Berman, G.P. and Kolovsky, A.R. (1983b): Phys. Lett. A95 15.CrossRefGoogle Scholar
  10. Berman, G.P. and Kolovsky, A.R. (1987a): Phys. Lett. A125 188.CrossRefGoogle Scholar
  11. Berman, G.P., Vlasova, O.F., and Izrailev, F.M. (1987b): Sov. Phys. JETP 66 269.Google Scholar
  12. Blumel, R., Fishman, S., Griniasti, M., and Smilansky, U. (1986): in “Quantum Chaos and Statistical Nuclear Physics”-Lectures Notes in Physics, Vol. 263 edited by T.H. Seligman and H. Nishioko (Springer-Verlag, Berlin)Google Scholar
  13. Blumel, R. and Smilansky, U. (1987): Z. Phys. D-Atoms, Molecules, and Clusters 6 83.ADSCrossRefGoogle Scholar
  14. Brown, R.C. and Wyatt, R.E. (1986): Phys. Rev. 57 1.MathSciNetADSGoogle Scholar
  15. Burns, M. (1991): Nonlinear Resonance in the Hydrogen Atom Ph.D. Dissertation, University of Texas at Austin.Google Scholar
  16. Burns, M. and Reichl, L.E. (1991): Nonlinear Resonance in the Microwave Driven Hydrogen Atom, Preprint, University of Texas at Austin.Google Scholar
  17. Casati, G., Chirikov, B.V., Izrailev, F.M., and Ford, J. (1979): in Stochastic Behavior in Classical and Hamiltonian SystemsLecture Notes in Physics, Vol. 93, edited by G.Casati and J.Ford. (Springer-Verlag, Berlin)Google Scholar
  18. Casati, G. Chirikov, B.V. and Shepelyansky, D.L. (1984): Phys. Rev. Lett. 53 2525.ADSCrossRefGoogle Scholar
  19. Casati, G., Chirikov, B.V., Shepelyansky, D.L., and Guarneri, I. (1987): Physics Reports 154 77.ADSCrossRefGoogle Scholar
  20. Casati, G. and Guarneri, I. (1984): Commun. Math. Phys. 95 121.MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. Chirikov, B., Izrailev, F.M., and Shepelyanskii, D. (1981): Sov. Sci. Rev. Sect.C2 209.zbMATHGoogle Scholar
  22. Comfeld, I.P., Fornin, S.V., and Sinai, Ya.G. (1982): Ergodic Theory (Springer-Verlag, Berlin).CrossRefGoogle Scholar
  23. Dyson, F.J. (1962a): J. Math. Phys. 3 140.MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. Dyson, F.J. (1962b): J. Math. Phys. 3 157.MathSciNetADSCrossRefGoogle Scholar
  25. Dyson, F.J. (1962c): J. Math. Phys. 3 166.MathSciNetADSCrossRefGoogle Scholar
  26. Feingold, M., Fishman, S., Grempel, D.R., and Prange, R.E. (1985): Phys. Rev. B31 6852.ADSGoogle Scholar
  27. Galvez, E.J., Sauer, B.E., Moorman, L., Koch, P.M., and Richards, D. (1988): Phys. Rev. Lett. 61 2011.ADSCrossRefGoogle Scholar
  28. Geisel, T., Radons, G., and Rubner, J. (1986): Phys. Rev. Lett. 57 2883.ADSCrossRefGoogle Scholar
  29. Grempel, D.R., Prange, R.E., and Fishman, S. (1984): Phys. Rev. A29 1639.ADSCrossRefGoogle Scholar
  30. Haake, F. (1990): Quantum Signatures of Chaos (Springer-Verlag, Berlin)Google Scholar
  31. Hose, G. and Taylor, H.S. (1983): Phys. Rev. Lett. 51 947.MathSciNetADSCrossRefGoogle Scholar
  32. Hose, G., Taylor, H.S., and Tip, A. (1984): J. Phys. A Math. Gen. 17 1203.MathSciNetADSCrossRefGoogle Scholar
  33. Izrailev, F.M. (1986): Phys. Rev. Lett. 56 541.ADSCrossRefGoogle Scholar
  34. Izrailev, F.M. and Shepelyanskii, D. (1979): Sov. Phys. Dokl. 24 996.ADSGoogle Scholar
  35. Izrailev, F.M. and Shepelyanskii, D. (1980): Theor. Math. Phys. 43 553.MathSciNetCrossRefGoogle Scholar
  36. Jensen, R.V., Susskind, S.M., and Sanders, M.M. (1989): Phys. Rev. Lett. 62 1476.ADSCrossRefGoogle Scholar
  37. Jose, J.V. and Cordery, R. (1986): Phys. Rev. Lett. 56 290.ADSCrossRefGoogle Scholar
  38. Koch, P. (1983): in Rydberg States of Atoms and Molecules, edited by R.F. Stebbings and F.B. Dunning (Cambridge University Press, Cambridge).Google Scholar
  39. Koch, P. (1988): in Electronic and Atomic Collisions, edited by H.B. Gilbody, W.R. Newell, F.H. Read, and A.C.H. Smith (Elsevier Science Publishers B.V., New York).Google Scholar
  40. Koch, P., Moorman, L., Sauer, B.E., Galvez, E.J., and van Leeuwen, K.A.H. (1989): Physica Scripta T26 59.Google Scholar
  41. Lin, W.A. and Reichl, L.E. (1987): Phys. Rev. A36 5099.ADSCrossRefGoogle Scholar
  42. Lin, W.A. and Reichl, L.E. (1988): Phys. Rev. A37 3972.ADSCrossRefGoogle Scholar
  43. Lin, W.A. and Reichl, L.E. (1989): Phys. Rev. A40 1055.ADSCrossRefGoogle Scholar
  44. Mehta, M.L. (1967): Random Matrices and the Statistical Theory of Energy Levels (Academic Press, New York)zbMATHGoogle Scholar
  45. Radons, G. and Prange, R.E. (1988): Phys. Rev. Lett. 61 1691.MathSciNetADSCrossRefGoogle Scholar
  46. Ramaswamy, R. (1984): J. Chem. Phys. 80 6194.ADSCrossRefGoogle Scholar
  47. Reichl, L.E. (1988): J. Stat. Phys. 53 41.MathSciNetADSCrossRefGoogle Scholar
  48. Reichl, L.E., Chen, Z.Y., Millonas, M.M. (1990): Phys. Rev.A41 1874.MathSciNetADSCrossRefGoogle Scholar
  49. Reichl, L.E. (1989): Phys. Rev. A39 4817.ADSCrossRefGoogle Scholar
  50. Reichl, L.E. and Li, H. (1990): Phys. Rev. A42 4543.MathSciNetADSCrossRefGoogle Scholar
  51. Reichl, L.E. and Lin, W.A. (1986): Phys. Rev. A33 3598.ADSCrossRefGoogle Scholar
  52. Sambe, H. (1973): Phys. Rev. A7 2203.ADSCrossRefGoogle Scholar
  53. Shepelyansky, D.L. (1985): in Chaotic Behavior in Quantum Systems edited by G. Casati (Plenum Press, New York).Google Scholar
  54. Shepelyansky, D.L. (1986): Phys. Rev. Lett. 56 677.MathSciNetADSCrossRefGoogle Scholar
  55. Shepelyansky, D.L. (1987): Physica 28D 103.Google Scholar
  56. Shirley, J.H. (1965): Phys. Rev. 139 979.ADSCrossRefGoogle Scholar
  57. Toda, M. and Ikeda, K. (1987): J. Phys. A20 3833.ADSGoogle Scholar
  58. van Leeuwen, K.A.H., Oppen, G.V., Renwick, S., Bowlin, J.B., Koch, P.M., Jensen, R.V., Rath, O., Richards, D., and Leopold, J.G. (1985): Phys. Rev. 55 2231.Google Scholar
  59. Zeldovich, Y.B. (1967): Sov. Phys. JETP 24 1006.ADSGoogle Scholar
  60. Zheng, W.M. and Reichl, L.E. (1987): Phys. Rev. A35 474.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • L. E. Reichl
    • 1
  1. 1.Center for Statistical Mechanics and Complex Systems, Department of PhysicsUniversity of Texas at AustinAustinUSA

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