Skip to main content
SpringerLink
Log in

Atomic and molecular physics experiments in quantum chaology

  • Conference paper
  • First Online:
Chaos and Quantum Chaos

Part of the book series: Lecture Notes in Physics ((LNP,volume 411))

Abstract

Several systems open to experimental study in atomic and molecular physics are furnishing important information about the behavior of a quantal system whose classical counterpart exhibits a transition to chaos. Some of these systems are autonomous (time-independent), and one gains information through detailed studies of their photoabsorption or stimulated-emission spectra. Others of these systems are time-dependent, being strongly driven by an external driving field. The aim of this paper is to review from the point of view of an actively involved experimenter our present understanding of the time-dependent process of the excitation and ionization of excited hydrogen atoms by a strong, linearly polarized microwave electric field. Many comparisons of experimental data with classical and quantal calculations have revealed six different regimes of dynamcal behavior in this periodically driven system. Certain scaling relationships present in the classical Hamiltonian dynamics for the driven Kepler system are found to be at least approximately obeyed in the corresponding quantal system, sometimes in surprising ways. Exploiting these scaling relationships has greatly facilitated the interpretation of experimental data, which reveal a number of fascinating phenomena.

To be published in the proceedings of Eighth South African Summer School in Theoretical Physics: Chaos and Quantum Chaos (13–24 January 1992, Blydepoort, Eastern Transvaal, Republic of South Africa) in the Springer-Verlag Lecture Notes in Physics series

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. For the classical, non-relativistic hydrogen atom, the principal action is I n = I r + I θ + I ϕ ; the total angular momentum is I t = I θ + I ϕ ; and the component of the angular momentum onto the polar axis is I m = I ϕ , with 2πI i = ∮ p i dr i for i = r, θ, and ϕ (and no sum convention); see Refs. [22,111]. The quantization conditions become I n = nh, I l = kh, and I m = mh. In the old quantum theory n = 1, 2, ... is the principal quantum number, and k is the subsidiary (or azimuthal) quantum number [22,124]. This is not k = 1, 2, ..., n, however, because modern quantization methods (Einstein-Brillouin-Keller) require k = l 1/2 with l = 0, 1, 2,. ..., n, in which the 1/2 refers not to the spin but to the Maslov (or Morse) index in semiclassical quantization. This index counts the number of classical turning points a encountered by a closed trajectory in the classical phase space; for a more general description in terms of caustics, see [12]. At each turning point a phase loss of π/2, which is equivalent to one-quarter of a wave, has to be taken into account. Continuity of the phase of the wavefunction then leads to I = (n+α/4)h. As one example, which is a case is usually associated with Wentzel-Kramers-Brillouin, it is well known that the one-dimensional harmonic oscillator, which has two turning points per period, has a ‘zero-point’ energy, i.e., a non-zero energy when v=0 in the quantized energy expression E v = (v+1/2)h, where v = 0, 1, .... For further reading and to see how this may be understood from conditions to be satisfied under a coordinate transformation of a path integral from Cartesian into spherical coordinates, requiring a new term h 2/4 in the classical Hamiltonian to be added to the angular momentum part |L|2 = l(l + 1)h 2, giving (l + 1/2)2 h 2, see p. 203 and p. 212 etc., of Ref. [59].

    Google Scholar 

  2. Secondary resonances are defined in a better way as the result of the perturbation Hamiltonian, and they give rise to secondary island chains in Poincaré sections of the phase space. An important difference between these resonances is that the strength of primary resonances depends only weakly on ε, namely as ε1/2, whereas for secondary resonances, it decreases much faster than this for small ε, where e is the (linear) interaction coupling parameter. See Chap. 2.4b of Ref. [97].

    Google Scholar 

  3. Andrei, E.Y. Yücel, S., and Menna, L. Phys. Rev. Lett. (1991) 67, 3704–7.

    Google Scholar 

  4. Arndt, M., Buchleitner, A., Mantegna, R.N., and Walther, H. (1991) Phys. Rev. Lett. 67, 2435–8.

    Google Scholar 

  5. Banks, D. and Leopold, J.G. (1978) J. Phys. B 11, 37–46 and 2833-43.

    Google Scholar 

  6. Bardsley, J.N., Szöke, A., and Comella, M.J. (1988) J. Phys B 21, pp. 3899ff.

    Google Scholar 

  7. Bayfield, J.E. and Koch, P.M. (1974) Phys. Rev. Lett. 33, 258.

    Google Scholar 

  8. Bayfield, J.E., Gardner, L.D., and Koch, P.M. (1977) Phys. Rev. Lett. 39, 76.

    Google Scholar 

  9. Bayfield, J.E. and Pinnaduwage, L.A. (1985) Phys. Rev. Lett. 54, 313–6.

    Google Scholar 

  10. Bayfield J.E., Casati G., Guarneri I., and Sokol D.W. (1989) Phys. Rev. Lett. 63, 364–7.

    Google Scholar 

  11. Bayfield, J.E. (1991) CHAOS 1, 110–113.

    Google Scholar 

  12. Berry, M. (1981) ‘Semiclassical Mechanics of Regular and Irregular Motion in Chaotic Behavior of Deterministic Systems', in Les Houches Lectures XXXVI, Eds.: G. Iooss, R.H.G. Helleman, and R. Stora, (North Holland, Amsterdam), pp. 171–271.

    Google Scholar 

  13. Berry, M. (1989) Physica Scripta 40, 335–6.

    Google Scholar 

  14. Berry M.V. (1989) Proc. Roy. Soc. London A423, 219–31.

    Google Scholar 

  15. Berry, M.V. (1991) in Chaos and Quantum Physics, Eds.: M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam).

    Google Scholar 

  16. Blümel, R. and Smilansky, U. (1987) Z. Phys. D 6, 83–105.

    Google Scholar 

  17. Blümel, R. and Smilansky, U. (1988) Phys. Rev. Lett. 60 (1988) 477–80.

    Google Scholar 

  18. Blümel, R. and Smilansky, U. (1988) in The Structure of Small Molecules and Ions, Eds.: R. Naaman and Z. Vager, (Plenum Press, New York), pp. 319–31.

    Google Scholar 

  19. Blümel, R., Graham, R., Sirko, L., Smilansky, U., Walther, H., and Yamada, K. (1989) Phys. Rev. Lett. 62, 341–4; Blümel, R., Buchleitner, A., Graham, R., Sirko, L., Smilansky, U., and Walther, H. (1991) Phys. Rev. A 44, 4521–40.

    Google Scholar 

  20. Blümel, R. and Smilansky, U. (1989) Physica Scripta 40, 386–93.

    Google Scholar 

  21. Blümel, R. and Smilansky, U. (1990) J. Opt. Soc. Am. B 7, 664–79.

    Google Scholar 

  22. Born, M. (1924) The Mechanics of the Atom, (republished by Frederick Ungar Publishing Co., New York, 1960).

    Google Scholar 

  23. Breuer, H.P., Dietz, K., and Holthaus, M. (1988) Z. Phys. D 8, 349–57.

    Google Scholar 

  24. Breuer, H.P., Dietz, K., and Holthaus, M. (1988) Z. Phys. D 10, pp. 13ff.

    Google Scholar 

  25. Breuer, H.P., Dietz, K., and Holthaus, M. (1989) J. Phys. B 22, 3187–96.

    Google Scholar 

  26. Breuer, H.P. and Holthaus, M. (1989) Z. Phys. D 11, 1–14.

    Google Scholar 

  27. Breuer, H.P. and Holthaus, M. (1989) Phys. Lett. A 140, 507–12.

    Google Scholar 

  28. Breuer, H.P., Dietz, K., and Holthaus, M. (1990) Nuovo Cimento 105B, pp. 53ff.

    Google Scholar 

  29. Breuer, H.P., Dietz, K., and Holthaus, M. (1990) J. Phys. France 51, pp. 709ff.

    Google Scholar 

  30. Breuer, H.P., Dietz, K., and Holthaus, M. (1991) Z. Phys. D 18, 239–48.

    Google Scholar 

  31. Breuer, H.P. and Holthaus, M. (1991) J. Phys. II 1, 437–49.

    Google Scholar 

  32. Breuer, H.P. and Holthaus, M. (1991) Annals of Physics 211, 249–91.

    Google Scholar 

  33. Brivio, G.P., Casati, G., Perotti, L., Guarneri, I. (1988) Physica D 33, 51–7.

    Google Scholar 

  34. Broyer, M., Delacrétaz, G., Ni, G.-Q., Whetten, R.L., Wolf, J.-P., and Wöste, L. (1989) Phys. Rev. Lett. 62, 2100–3.

    Google Scholar 

  35. Buchleitner, A., Sirko, L., and Walther, H. (1991) Europhys. Lett. 16, 35–40.

    Google Scholar 

  36. Burgdörfer, J. and Bottcher, C. (1988) Phys. Rev. Lett. 61, 2917–20; Kemmler, J., Burgdörfer, J., and Reinhold, C.O. (1991) Phys. Rev. A 44, pp. 2933ff.

    Google Scholar 

  37. Casati, G., Chirikov, B.V., Guarneri, I., and Shepelyansky, D.L. (1987) Phys. Rev. Lett. 59, 2927–30.

    Google Scholar 

  38. Casati, G., Chirikov, B.V., Guarneri, I., and Shepelyansky, D.L. (1987) Phys. Rep 154, 77–123.

    Google Scholar 

  39. Casati, G., Guarneri, I., and Shepelyansky, D.L. (1988) I.E.E.E. J. Quantum Electron. 24 1420–45.

    Google Scholar 

  40. Casati, G., Guarneri, I., and Shepelyansky, D.L. (1990) Physica A 163, pp. 205ff.

    Google Scholar 

  41. Chen, Y., Halle, S., Jonas, D.M., Kinsey, J.L., and Field, R.W. (1990) J. Opt. Soc. Am. B7, 1805–1815.

    Google Scholar 

  42. Chirikov, B.V. (1979) Phys. Rep. 52, 263–379.

    Google Scholar 

  43. Chirikov, B.V. (1991) in Chaos and Quantum Physics, Eds.: M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam), pp. 443–545.

    Google Scholar 

  44. Chu, S.-I. (1988) Adv. Chem. Phys. 73, pp. 2799ff; see also (1985) Adv. At. Mol. Phys. 21, pp. 197ff.

    Google Scholar 

  45. Dando, P.A., and Richards, D. (1990) J. Phys. B. 23, 3179.

    Google Scholar 

  46. Delande, D. and Gay, J.C. (1987) Phys. Rev. Lett. 59, 1809–12.

    Google Scholar 

  47. Feingold, M., Littlejohn, R.G., Solina, S.B., Pehling, J.S., and Piro, 0. (1990) Phys. Lett. A 146, 199–203.

    Google Scholar 

  48. Ford, J., Mantica, G., and Ristow, G.H. (1990) in Chaos / XAOC, Proceedings of a Soviet-American Conference, Ed.: D. K. Campbell (American Institute of Physics, New York), pp. 477–493.

    Google Scholar 

  49. Friedrich, H. and Wintgen, D. (1989) Phys. Rep. 183, 37–79.

    Google Scholar 

  50. Fu, P., Scholz, T.J., Hettema, J.M., and Gallagher, T.F. (1990) Phys. Rev. Lett. 64, 571–4.

    Google Scholar 

  51. Gajda, M., Grochmalicki, J., Lewenstein, M., and Rzążewski, K. (1992) Phys. Rev. A 4, 1638–53.

    Google Scholar 

  52. Galvez, E.G., Sauer, B.E., Moorman, L., Koch, P.M., and Richards, D. (1988) Phys. Rev. Lett. 61 2011–4.

    Google Scholar 

  53. Gay, J.-C., Editor, Irregular Atomic Systems and Quantum Chaos (1992) (Gordon and Breach, Montreux). This is a reprinting of articles that appeared in the two combined numbers of Vol. 25 of the journal Comments in Atomic and Molecular Physics (Nos. 1–3, 1991 and Nos. 4–6,1992).

    Google Scholar 

  54. Goldstein, H. (1950) Classical Mechanics, (Addison-Wesley, 12th printing, 1977).

    Google Scholar 

  55. Gomez Llorente, J.M., Taylor, H.S., and Pollak, E. (1989) Phys. Rev. Lett. 62, 2096–9.

    Google Scholar 

  56. Gontis, V. and Kaulakys, B. (1987) J. Phys. B 20, 5051–64.

    Google Scholar 

  57. Graham, R. (1988) Europhys. Lett. 7, 671–75.

    Google Scholar 

  58. Grimes, C.C., Brown, T.R., Burns, M.L., and Zipfel, C.L. (1976) Phys. Rev. B 13, 140–47.

    Google Scholar 

  59. Gutzwiller, M.C. (1990) Chaos in Classical and Quantum Mechanics, (Springer Verlag, New York).

    Google Scholar 

  60. Halbach, K. and Holsinger, R.F. (1976) Part. Accel. 7, 213–22.

    Google Scholar 

  61. Hasegawa, H., Robnik, M., and Wunner, G. (1989) Prog. Theor. Phys. Suppl. 98, pp. 198ff. The volume in which this review article appears was devoted to New Trends in Chaotic Dynamics of Hamiltonian Systems and contains other articles on related problems.

    Google Scholar 

  62. Heller, E.J. (1984) Phys. Rev. Lett. 53, 1515–8.

    Google Scholar 

  63. Howard, J. (1991) Phys. Lett. A 156, 286–92.

    Google Scholar 

  64. Howard, J. (1992) Phys. Rev. A 46, 364–72.

    Google Scholar 

  65. Iu, C.-h., Welch, G.R., Kash, M.M., Kleppner, D., Delande, D., and Gay, J.C. (1991) Phys. Rev. Lett. 66, 145–8.

    Google Scholar 

  66. Jensen, R.V. (1982) Phys. Rev. Lett. 49, 1365–8.

    Google Scholar 

  67. Jensen, R.V. (1984) Phys. Rev. A 30, 386–97.

    Google Scholar 

  68. Jensen, R.V. (1987) Physica Scripta 35, pp. 668ff.

    Google Scholar 

  69. Jensen, R.V., Susskind, S.M., and Sanders, M.M. (1989) Phys. Rev. Lett. 62, 1476–9.

    Google Scholar 

  70. Jensen, R.V., Sanders, M.M., Saraceno, M., and Sundaram, B. (1989) Phys. Rev. Lett. 63, 2771–4.

    Google Scholar 

  71. Jensen, R.V. and Sundaram, B. (1990) Phys. Rev. Lett. 65, 1964–7.

    Google Scholar 

  72. Jensen, R.V., Susskind, S.M., and Sanders, M.M. (1991) Phys. Rep. 201, 1–56.

    Google Scholar 

  73. Kleppner, D., Littman, M.G., and Zimmerman, M.L. (1983) in Rydberg States of Atoms and Molecules, Eds.: R.F. Stebbings and F.B. Dunning (Cambridge University Press, New York), pp. 73–116.

    Google Scholar 

  74. Koch, P.M. and Mariani, D.R. (1980) J. Phys. B 13, L645–50.

    Google Scholar 

  75. Koch, P.M. and Mariani, D.R. (1981) Phys. Rev. Lett. 46, 1275–8.

    Google Scholar 

  76. Koch, P.M. (1982) J. Physique Colloq. 43, C2-187–C2-210.

    Google Scholar 

  77. Koch, P.M. (1983) in Rydberg States of Atoms and Molecules, Eds.: R.F. Stebbings and F.B. Dunning (Cambridge University Press, New York), pp. 473–512.

    Google Scholar 

  78. Koch, P.M., in Fundamental Aspects of Quantum Theory, Eds.: V. Gorini and A. Frigerio, (Plenum, New York, 1986).

    Google Scholar 

  79. Koch, P.M., Leeuwen, K.A.H., Rath, O., Richards, D., and Jensen, R.V. (1987) in The Physics of Phase Space, Eds.: Y.S. Kim and W.W. Zachary, Lecture Notes in Physics vol. 278 (Springer-Verlag, Berlin), pp. 106–13.

    Google Scholar 

  80. Koch, P.M. (1988) in Electronic and Atomic Collisions, Eds.: H.B. Gilbody, W.R. Newell, F.H. Read, and A.C.H. Smith, (North-Holland, Amsterdam), pp. 501–16.

    Google Scholar 

  81. Koch, P.M., Moorman, L., Sauer, B.E., and Galvez, E.J. (1989) Classical Dynamics in Atomic and Molecular Collisions, Eds.: T. Grozdanov, P. Grujić, and P. Kristić, (World Scientific, Singapore), pp. 348–67.

    Google Scholar 

  82. Koch P.M., Moorman L., Sauer B.E., Galvez E.J., and Leeuwen K.A.H. van (1989) Physica Scripta T26, 51–7.

    Google Scholar 

  83. Koch, P.M. (1990) in Chaos / XAOC, Proceedings of a Soviet-American Conference, Ed.: D. K. Campbell (American Institute of Physics, New York), pp. 441–475.

    Google Scholar 

  84. Koch, P.M. (1990) in The Ubiquity of Chaos, Ed.: S. Krasner (American Association for the Advancement of Science Press, Washington), pp. 75–97.

    Google Scholar 

  85. Koch, P.M., Moorman, L., Sauer, B.E. (1990) Comm. At. Mol. Phys. 25, 165–83.

    Google Scholar 

  86. Koch, P.M. (1992) CHAOS 2, 131–144.

    Google Scholar 

  87. Koch, P.M. and Leeuwen, K.A.H. van (1992), submitted for publication.

    Google Scholar 

  88. Kolmogorov, A.N. (1954) Dokl. Akad. Nauk. SSSR 98 pp. 527ff.; Moser, J. (1962) Nachr. Akad. Wiss. Göttingen Kl. II, n°1, 1; Arnold, V.I. (1963) Usp. Mat. Nauk. SSSR 18, pp. 13ff, and English translation in (1963) Russian Math. Surv. 18, pp. 85ff.

    Google Scholar 

  89. Landau, L.D. and Lifshitz, E.M. (1960) Classical Mechanics, (Pergamon Press, Oxford, 1977 printing).

    Google Scholar 

  90. Landau, L.D. and Lifshitz, E.M. (1977) Quantum Mechanics, 3rd edition, (Pergamon Press, Oxford), pp. 120ff.

    Google Scholar 

  91. Leeuwen, K.A.H. van, 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. Lett. 55, 2231–4.

    Google Scholar 

  92. Leopold, J.G. and Percival, I.C. (1978) Phys. Rev. Lett. 41, 944–7.

    Google Scholar 

  93. Leopold, J.G. and Percival, I.C. (1979) J. Phys. B 21, 2179–204.

    Google Scholar 

  94. Leopold, J.G. and Richards, D. (1989) J. Phys. B 22, 1931–61.

    Google Scholar 

  95. Leopold, J.G. and Richards, D. (1990) J. Phys. B 23, 2911–27.

    Google Scholar 

  96. Leopold, J.G. and Richards, D. (1991) J. Phys. B 24, 1209–40.

    Google Scholar 

  97. Lichtenberg, A.J. and Lieberman, M.A. (1983) Regular and Stochastic Motion, (Springer-Verlag, New York).

    Google Scholar 

  98. Lombardi, M., Pique, J.P., Labastie, P., Broyer, M., and Seligman, T. (1992) in Ref. [53].

    Google Scholar 

  99. MacKay, R.S. and Meiss, J.D. (1988) Phys. Rev. A 37, 4702–7.

    Google Scholar 

  100. Main, J., Wiebusch, G., and Welge, K.H. (1991) Comm. At. Mol. Phys. 25, 233–51.

    Google Scholar 

  101. Meerson, B.I., Oks, E.A., and Sasorov, P.V. (1979) Pis'ma Zh. Eksp. Teor. Fiz. 29, 79–82 [Sov. Phys.-JETP Lett. 29, 72-5].

    Google Scholar 

  102. Meiss, J.D. (1989) Phys. Rev. Lett. 62, 1576.

    Google Scholar 

  103. Moorman, L., Galvez, E.J., Sauer, B.E., Mortazawi-M, A., Leeuwen, K.A.H. van, Oppen, G.v., and Koch, P.M. (1988) Phys. Rev. Lett. 61, 771–4.

    Google Scholar 

  104. Moorman, L., Galvez, E.J., Sauer, B.E., Mortazawi-M., A., Leeuwen, K.A.H. van, Oppen, G.v., and Koch, P.M. (1989) in Atomic Spectra and Collisions in External Fields, Vol. 2, Eds.: K.T. Taylor, M.H. Nayfeh, and C.W. Clark, (Plenum Press, New York), pp. 343–57.

    Google Scholar 

  105. Moorman, L. (1991) in The Electron, Ed.: A. Weingartshofer, (Kluwer, Dordrecht).

    Google Scholar 

  106. Moorman, L. and Koch, P.M. (1992) in Quantum Nonintegrability, Eds.: D.H. Feng and J. M. Yuan, Vol. 4 in Directions in Chaos, Series Editor: Bai-Lin Hao (World Scientific, Singapore, in press).

    Google Scholar 

  107. Nauenberg, M. (1990) Phys. Rev. Lett. 64, 2731; and (1990) Europhys. Lett. 13, 611-6.

    Google Scholar 

  108. O'Connor, P.W., Gehlen, J.N., Heller, E.J. (1987) Phys. Rev. Lett. 58, 1296–9.

    Google Scholar 

  109. Oppenheimer, J.R. (1928) Phys. Rev. 31, pp. 66ff.

    Google Scholar 

  110. Ozorio de Almeida, A.M. (1988) Hamiltonian Systems: Chaos and Quantization, (Cambridge University Press, Cambridge).

    Google Scholar 

  111. Percival I.C. and Richards, D. (1975) Adv. At. Mol. Phys. 11, 1–82.

    Google Scholar 

  112. Radons, G. and Prange, R.E. (1988) Phys. Rev. Lett. 61, 1691–4.

    Google Scholar 

  113. Rath, 0. and Richards, D., in preparation.

    Google Scholar 

  114. Reinhold, C.O., Burgdörfer, J., and Kemmler, J. (1992) Phys. Rev. A 45, R2655–8.

    Google Scholar 

  115. Richards, D. (1987) J. Phys. B 20, 2171–92.

    Google Scholar 

  116. Richards, D., Leopold, J.G., Koch, P.M., Galvez, E.J., Leeuwen, K.A.H. van, Moorman, L., Sauer, B.E., and Jensen, R.V. (1989) J. Phys. B 22, 1307–33.

    Google Scholar 

  117. Richards, D. (1990) in Aspects of Electron-Molecule Scattering and Photoionization, Ed.: A. Herzenberg, AIP Conference Proceedings 204, 45–64.

    Google Scholar 

  118. Richards, D. and Leopold, J.G. (1990) in The Physics of Electronic and Atomic Collisions, Eds.: A. Dalgarno, R.S. Freund, P.M. Koch, M.S. Lubell, and T.B. Lucatorto (AIP Conf. Proc. 205), pp. 492–8.

    Google Scholar 

  119. Ruff, G.A., Dietrick, K.M., and Gallagher, T.F. (1990) Phys. Rev. A 42, 5648–51.

    Google Scholar 

  120. Sanders, M.M., Jensen, R.V., Koch, P.M., and Leeuwen, K.A.H. van (1987) Nucl. Phys. B (Proc. Suppl.) 2, 578–9.

    Google Scholar 

  121. Sauer, B.E., Leeuwen, K.A.H. van, Mortazawi-M., A., and Koch, P.M. (1991) Rev. Sci. Instr. 62, 189–97.

    Google Scholar 

  122. Sauer, B.E., Yoakum, S., Moorman, L., Koch, P.M., Richards, D., and Dando, P.A. (1992) Phys. Rev. Lett. 68, 468–71.

    Google Scholar 

  123. Sauer, B.E., Bellermann, M.R.W., and Koch, P.M. (1992) Phys. Rev. Lett. 68, 1633–6.

    Google Scholar 

  124. Series, G.W. (1988) The Spectrum of the Hydrogen Atom: Advances, (World Scientific, Singapore), pp. 20–4.

    Google Scholar 

  125. Shepelyansky, D.L. (1985) in Chaotic Behavior in Quantum Systems, Ed.: G. Casati, (Plenum, New York), NATO ASI Series B, Vol. 120, pp. 187–204.

    Google Scholar 

  126. Stevens, M.J. and Sundaram, B. (1989) Phys. Rev. A 39, 2862–77.

    Google Scholar 

  127. 'Irregular’ here means chaotic, in the sense of exponential instability, for a finite time duration, as opposed to an infinite time duration; see e.g., T. Tél, ‘Transient Chaos', in (1990) Directions in Chaos, Vol. 3, Ed.: Hao Bai-lin (World Scientific, Singapore), pp. 149ff.

    Google Scholar 

  128. Wang, K. and Chu, S-I. (1989) Phys. Rev. A 39, 1800–8.

    Google Scholar 

  129. Waterland, R.L., Yuan, Jian-Min, Martens, C.C., Gillilan, E., and Reinhardt, W.P. (1989) Phys. Rev. Lett. 61, 2733–6.

    Google Scholar 

  130. Wintgen, D. and Hönig, A. (1989) Phys. Rev. Lett. 63, 1467–70.

    Google Scholar 

  131. Wintgen, D., Richter, K., and Tanner, G. (1992) CHAOS 2, 19–33.

    Google Scholar 

  132. Wolf, A., Swift, J.B., Swinney, H.L., and Vastano, J.A., (1985) Physica D 16, 285–317.

    Google Scholar 

  133. Yamazaki, Y., Stolterfoht, N., Miller, P.D., Krause, H.F., Pepmiller, P.L., Datz, S., Sellin, I.A., Scheurer, J.N., Andriamonje, S., Bertault, D., and Chemin, J.F. (1988) Phys. Rev. Lett. 61, 2913–6.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, State University of New York at Stony Brook, 11794-3800, Stony Brook, NY, USA

    Peter M. Koch

Authors
  1. Peter M. Koch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

W. Dieter Heiss

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Verlag

About this paper

Cite this paper

Koch, P.M. (1992). Atomic and molecular physics experiments in quantum chaology. In: Heiss, W.D. (eds) Chaos and Quantum Chaos. Lecture Notes in Physics, vol 411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56253-2_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-56253-2_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56253-5

  • Online ISBN: 978-3-540-47495-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation