Periodic Orbits and Recurrences: An Introduction and Review

  • J. B. Delos
Part of the Few-Body Systems book series (FEWBODY, volume 7)


The study of periodic classical orbits of quantum systems is a branch of the field called “quantum chaos,” which is the study of quantum-mechanical systems whose classical counterparts exhibit chaotic motion. Many examples have now been examined: a one-electron atom in magnetic field[1], an atom in an oscillating electric field[2], any molecule in a high vibrational state[3], a “quantum billiard,” such as an electron in a stadium-shaped microjunction[4], and numerous model systems, including the Henon-Heiles oscillator[5], quantum maps[6], or geodesic motion of a particle on a surface of constant negative curvature[7]. Always the central issues are: How do we use information about classical orbits to generate information about quantum wave-functions? Can we interpret observations on a quantum system using classical or semiclassical mechanics? How does classically chaotic behavior manifest itself in quantum properties of a system?


Periodic Orbit Quantum Property Maslov Index Conductance Spectrum Geodesic Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. L. Du and J. B. Delos, Phys. Rev. A 38, 1896 and 1912 (1988); D. Wintgen and H. Friedrich, Phys. Rev. A35, 1464 (1987 or 36, 131 (1987).ADSCrossRefGoogle Scholar
  2. 2.
    J. Bayfield and P. Koch, Phys. Rev. Lett 33, 258 (1974); R. V. Jensen, Phys. Rev. A30, 386 (1984); N. B. Delone, V. P. Krainov and D. L. Shepelyanskii, Sov. Phys. Usp. 26, 551 (1983).ADSCrossRefGoogle Scholar
  3. 3.
    D. W. Noid, M. L. Koszykowski and R. Marcus, Ann. Rev. Phys. Chem. 32, 267 (1981).ADSCrossRefGoogle Scholar
  4. 4.
    a) R. V. Jensen, Chaos 1, 101 (1991). b) C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins and A. C. Gossard, Phys. Rev. Lett 69, 506 (1992).MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    N. Pomphrey, J. Phys. B7, 1909 (1974); R. T. Swimm and J. B. Delos, J. Chem. Phys. 71, 1706 (1979).ADSGoogle Scholar
  6. 6.
    M. V. Berry, N. L. Balazs, M. Tabor and A. Voros, Ann. Phys. (N.Y.) 26, 122 (1979).MathSciNetGoogle Scholar
  7. 7.
    N. L. Balazs and A. Voros, Phys. Reports 143, 109 (1986); R. Aurich and F. Steiner, DESY preprint 91–044 (1991).Google Scholar
  8. 8.
    M. Gutzwiller, Chaos in Classical Quantum Mechanics. Springer (1990); A. M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization. Cambridge (1988); F. Haake, Quantum Signatures of Chaos. Springer, Berlin (1991); L. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations. Springer (1992); K. Nakamura, Quantum Chaos: a new paradigm of nonlinear dynamics. Cambridge (1993).Google Scholar
  9. 9.
    J. Main, G. Wiebusch, A. Holle and K. H. Welge, Phys. Rev. Lett. 57, 2789 (1986); A. Holle, J. Main, G. Wiebusch, H. Rottke and K. H. Welge, Phys. Rev. Lett. 61, 161 (1988).ADSCrossRefGoogle Scholar
  10. 10.
    K. R. Meyer, Tras. Am. Math. Soc. 149, 95 (1970); J. M. Mao and J. B. Delos, Phys. Rev. A45, 1746 (1992); J. Main, G. Wiebusch, K. Welge, J. Shaw and J. B. Delos, Phys. Rev. A (accepted).MATHCrossRefGoogle Scholar
  11. 11.
    C. R. LeSueur, J. R. Henderson and J. Tennyson, Chem. Phys. Lett. 206, 429 (1993).ADSCrossRefGoogle Scholar
  12. 12.
    E. Bogomolnyi, Physica D31, 169 (1988); D. Provost and M. Baranger, Phys. Rev. Lett. 21, 662 (1993).ADSGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1994

Authors and Affiliations

  • J. B. Delos
    • 1
  1. 1.Physics DepartmentCollege of William and MaryWilliamsburgUSA

Personalised recommendations