Quantum-classical correspondence via Liouville dynamics. II. Correspondence for chaotic Hamiltonian systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 55, Issue 1, 1997, Pages 43-61

  Wilkie, Joshua ^a   Brumer, Paul ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001694428     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.55.43     Document Type: Article

References (39)

1. L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Nonrelativistic Theory (Pergamon Press, London, 1958); E. Merzbacher, Quantum Mechanics (Wiley, New York, 1961).
2. M.V. Berry, Philos. Trans. R. Soc. London Ser. A 287, 237 (1977).
3. C. Jafféand P. Brumer, J. Chem. Phys. 82, 2330 (1985).
4. M.V. Berry, J. Phys. A 10, 2083 (1977).
5. J. Wilkie and P. Brumer, preceding paper, Phys. Rev. A 54, 27 (1996) (referred to as paper I).
6. J. Ford and M. Ilg, Phys. Rev. A 45, 6165 (1992).
7. M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, 1966).
8. Current semiclassical theories for irregular systems have been shown to approximate the Hamiltonian eigenvalues and eigenfunctions of low lying eigenstates with considerable accuracy. See, for example, R. Aurich, C. Matthies, M. Sieber and F. Steiner, Phys. Rev. Lett. 68, 1629 (1992);
9. D. Provost and M. Baranger, Phys. Rev. Lett. 71, 662 (1993).
10. M.V. Berry, in Chaos and Quantum Physics, edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam, 1991).
11. J. Wilkie and P. Brumer, Phys. Rev. E 49, 1968 (1994).
12. A. Pattanayak and P. Brumer, Phys. Rev. Lett. 77, 59 (1996).
13. C. Jafféand P. Brumer, J. Phys. Chem. 88, 4829 (1984).
14. S.R. De Groot and L.G. Suttorp, Foundations of Electrodynamics (North-Holland, Amsterdam, 1972).
15. V.I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Addison-Wesley, New York, 1989).
16. The Dirac formulation of density matrix dynamics was first discussed by U. Fano, Rev. Mod. Phys. 29, 74 (1957). See A. Royer, Phys. Rev. A 43, 44 (1991);
17. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995) and references therein for more recent developments including a discussion of representation theory.
18. N.L. Balazs and B.K. Jennings, Phys. Rep. 104, 347 (1984).
19. S.S. Mizrahi, Physica A 127, 241 (1984).
20. P. Cvitanovic and B. Eckhardt, J. Phys. A 24, L237 (1991);
21. P. Cvitanovic, Physica D 51, 138 (1991); B. Eckhardt, in Quantum Chaos, edited by G. Casati, I Guarneri, and U. Smilansky (North-Holland, Amsterdam, 1993).
22. J. Wilkie and P. Brumer (unpublished).
23. H. Goldstein, Classical Mechanics (Addison-Wesley, New York, 1950).
24. J.M. Robbins and M.V. Berry, J. Phys. A 25, L961 (1992).
25. A. Voros, in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, edited by G. Casati and J. Ford (Springer, Berlin, 1979).
26. M.V. Berry, Proc. R. Soc. London Ser. A 423, 219 (1989).
27. K.G. Kay, J. Chem. Phys. 79, 3026 (1983).
28. J.H. Hannay and A.M. Ozorio de Almeida, J. Phys. A 17, 3429 (1984).
29. I.C. Percival, Adv. Chem. Phys. 36, 1 (1977);
30. J.B. Delos, Adv. Chem. Phys. 65, 161 (1986).
31. S.C. Creagh, J.M. Robbins and R.G. Littlejohn, Phys. Rev. A 42, 1907 (1990);
32. B. Eckhardt and D. Wintgen, J. Phys. A 24, 4335 (1991);
33. J.M. Robbins, Nonlinearity 4, 343 (1991).
34. M.V. Berry, Proc. R. Soc. London Ser. A 400, 229 (1985). For discussions of the convergence problem see: M.V. Berry and J.P. Keating, ibid. 437, 151 (1992);
35. O. Agam and S. Fishman, J. Phys. A 26, 2113 (1993).
36. M. Feingold and A. Peres, Phys. Rev. A 34, 591 (1986).
37. P. Pechukas, Phys. Rev. Lett. 51, 943 (1983).
38. D.M. Wardlaw, D.W. Noid and R.A. Marcus, J. Phys. Chem. 88, 536 (1984).
39. Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1965).