HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 115 (2006) > Number 3
| Next Article >

Prog. Theor. Phys. Vol. 115 No. 3 (2006) pp. 523-546

[ Full Text PDF : FREE ACCESS (1270K) ]

Semiclassical Approach for Bifurcations in a Smooth Finite-Depth Potential

Alexander G. Magner,1,3,4,5 Ken-ichiro Arita2 and Sergey N. Fedotkin4,5

1Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
2Department of Physics, Nagoya Institute of Technology, Nagoya 466-8555, Japan
3Laboratoire de Spectrométrie Physique, Université Joseph-Fourier-Grenoble, F-38402 Saint-Martin-d'Hères Cedex, France
4Institute for Nuclear Research, 03680, Prospekt Nauki 47, Kiev-28, Ukraine
5Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany

(Received September 12, 2005)

Abstract:

The analytical trace formula for a dense cascade of bifurcations was derived using the improved stationary phase method based on extensions of the semiclassical Gutzwiller path integral approach. For the integrable version of the famous Hénon-Heiles Hamiltonian, our analytical trace formula solves all bifurcation problems, in particular, in the harmonic oscillator limit and the potential barrier limit. We obtain nice agreement with quantum results for gross to finer shell structures in level densities and for the shell structure energies, even near the potential barrier where there is a rather dense sequence of bifurcations.


URL : http://ptp.ipap.jp/link?PTP/115/523/
DOI : 10.1143/PTP.115.523

[ Full Text PDF : FREE ACCESS (1270K) ] Citation:

References:

  1. M. C. Gutzwiller, J. Math. Phys. 12 (1971), 343, [CrossRef]and earlier references quoted therein.
  2. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1990).
  3. R. B. Balian and C. Bloch, Ann. of Phys. 69 (1972), 76[CrossRef].
  4. V. M. Strutinsky, Nukleonika 20 (1975), 679.
    V. M. Strutinsky and A. G. Magner, Sov. Phys. Part. Nucl. 7 (1977), 138.
  5. M. V. Berry and M. Tabor, Proc. R. Soc. London A 349 (1976), 101.
  6. M. V. Berry and M. Tabor, J. of Phys. A 10 (1977), 371[CrossRef].
  7. V. M. Strutinsky, A. G. Magner, S. R. Ofengenden and T. Døssing, Z. Phys. A 283 (1977), 269.
  8. S. C. Creagh and R. G. Littlejohn, Phys. Rev. A 44 (1990), 836[APS]; J. of Phys. A 25 (1992), 1643[CrossRef].
  9. M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley Reading, 1997).
  10. A. G. Magner, S. N. Fedotkin, K. Arita, K. Matsuyanagi, T. Misu, T. Schachner and M. Brack, Prog. Theor. Phys. 102 (1999), 551[PTP].
  11. A. G. Magner, S. N. Fedotkin, K. Arita, K. Matsuyanagi and M. Brack, Phys. Rev. E 63 (2001), 065201[APS](R).
  12. A. G. Magner, K. Arita, S. N. Fedotkin and K. Matsuyanagi, Prog. Theor. Phys. 108 (2002), 853[PTP].
  13. M. V. Fedoryuk, Sov. J. Comp. Math. and Math. Phys. 4 (1964), 671; ibid. 10 (1970), 286.
  14. V. P. Maslov, Theor. Math. Phys. 2 (1970), 30.
  15. M. V. Fedoryuk, Saddle-point method (Nauka, Moscow, 1977), in Russian.
  16. M. V. Fedoryuk, Asymptotics: Integrals and sums (Nauka, Moscow, 1987), in Russian.
  17. C. Chester, B. Friedmann and F. Ursell, Proc. Cambridge Philos. Soc. 53 (1957), 599.
  18. S. Tomsovic, M. Grinberg and D. Ullmo, Phys. Rev. Lett. 75 (1995), 4346[APS].
    D. Ullmo, M. Grinberg and S. Tomsovic, Phys. Rev. E 54 (1996), 136[APS].
  19. M. Sieber, J. of Phys. A 30 (1997), 4563[CrossRef].
  20. P. Meier, M. Brack and C. Creagh, Z. Phys. D 41 (1997), 281.
  21. H. Schomerus and M. Sieber, J. of Phys. A 30 (1997), 4537[CrossRef].
  22. M. Sieber and H. Schomerus, J. of Phys. A 31 (1998), 165[CrossRef].
  23. H. Schomerus, J. of Phys. A 31 (1998), 4167[CrossRef].
  24. M. Brack, P. Meier and K. Tanaka, J. of Phys. A 32 (1999), 331[CrossRef].
  25. M. Brack, S. Fedotkin, A. G. Magner and M. Mehta, J. of Phys. A 36 (2003), 1095[CrossRef].
  26. J. Kaidel and M. Brack, Phys. Rev. E 70 (2004), 016206[APS].
  27. A. M. Ozorio de Almeida and J. H. Hannay, J. of Phys. A 20 (1987), 5873[CrossRef].
  28. A. M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, Cambridge, 1988).
  29. S. C. Creagh, Ann. of Phys. 248 (1996), 60[CrossRef].
  30. M. Brack, Foundations of Physics 31 (2001), 209.
  31. M. Brack, M. Mehta and K. Tanaka, J. of Phys. A 34 (2001), 8199[CrossRef].
  32. J. Kaidel, P. Winkler and M. Brack, Phys. Rev. E 70 (2004), 066208[APS].
  33. V. M. Strutinsky, Nucl. Phys. A 95 (1967), 420[CrossRef]; ibid. 122 (1968), 1[CrossRef].
  34. M. Brack, private communications (2005).
  35. L. D. Landau and E. M. Lifshits, Mechanics, Third edition (Pergamon Press Ltd., 1976).
  36. A. D. Bruno, Math. USSR Sbornik 12 (1970), 271; Inst. Prikl. Mat. Akad. Nauk SSSR. Preprint No. 18 (Moskow, 1972), in Russian.
  37. M. Abramowitz and I. A. Stegun, Handbook of mathematical functions (Dover publications INC., New York, 1964).
  38. A. M. Ozorio de Almeida, C. H. Lewkopf and S. Tomsovic, J. of Phys. A 35 (2002), 10629[CrossRef].
  39. F. A. Ivanyuk and V. M. Strutinsky, Z. Phys. A 290 (1979), 107.
  40. F. A. Ivanyuk, Z. Phys. A 316 (1984), 237.
  41. T. Vertse, A. T. Kruppa and W. Nazarewicz, Phys. Rev. C 61 (2000), 064317[APS].
  42. T. Vertse, A. T. Kruppa, R. J. Liotta, W. Nazarewicz, N. Sandulescu and T. R. Werner, Phys. Rev. C 57 (1998), 3089[APS].

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.