Skip to main content
SpringerLink
Log in

Semiclassical Description of Shell Effects in Finite Fermion Systems

  • Chapter
  • First Online:
Advances in Solid State Physics

Part of the book series: Advances in Solid State Physics Volume 41 ((ASSP,volume 41))

Abstract

Since its first appearance in 1971, Gutzwiller’s trace formula has been extended to systems with continuous symmetries, in which not all periodic orbits are isolated. In order to avoid the divergences occurring in connection with symmetry breaking and orbit bifurcations (characteristic of systems with mixed classical dynamics), special uniform approximations have been developed. We first summarize some of the recent developments in this direction. Then we present applications of the extended trace formulae to describe prominent gross-shell effects of various finite fermion systems (atomic nuclei, metal clusters, and a mesoscopic device) in terms of the leading periodic orbits of their suitably modeled classical mean-field Hamiltonians.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. C. Gutzwiller, J. Math. Phys. 12, 343 (1971); and earlier references quoted therein

    Article  Google Scholar 

  2. M. C. Gutzwiller: Chaos in classical and quantum mechanics (Springer, New York, 1990)

    Google Scholar 

  3. Chaos Focus Issue on Periodic Orbit Theory, Chaos, Vol. 2, No. 1 (1992)

    Google Scholar 

  4. Quantum Chaos Y2K, Proceedings of Nobel Symposium 116, K.-F. Berggren and S. Åberg (Eds.), Physica Scripta Vol. T90 (2001)

    Google Scholar 

  5. R. Balian, and C. Bloch, Ann. Phys. (N. Y.) 69, 76 (1972)

    Article  Google Scholar 

  6. H. Nishioka, K. Hansen, and B. R. Mottelson, Phys. Rev. B 42, 9377 (1990)

    Article  CAS  Google Scholar 

  7. J. Pedersen, S. Bjørnholm, J. Borggreen, K. Hansen, T. P. Martin, and H. D. Rasmussen, Nature 353, 733 (1991)

    Article  CAS  Google Scholar 

  8. M. Brack, Rev. Mod. Phys. 65, 677 (1993)

    Article  CAS  Google Scholar 

  9. M. V. Berry and M. Tabor, Proc. R. Soc. Lond. A 349, 101 (1976)

    Article  Google Scholar 

  10. E. N. Bogachek and G. A. Gogadze, Sov. Phys. JETP 36, 973 (1973)

    Google Scholar 

  11. M. V. Berry and M. Tabor, Proc. R. Soc. Lond. A 356, 375 (1977)

    Google Scholar 

  12. V. M. Strutinsky, Nukleonika (Poland) 20, 679 (1975) V. M. Strutinsky and A. G. Magner, Sov. J. Part. Nucl. 7, 138 (1976)

    Google Scholar 

  13. V. M. Strutinsky, A. G. Magner, S. R. Ofengenden, and T. Døssing, Z. Phys. A 283, 269 (1977)

    Article  Google Scholar 

  14. M. Brack and R. K. Bhaduri: Semiclassical Physics, Frontiers in Physics Vol. 96 (Addison-Wesley, Reading, USA, 1997)

    Google Scholar 

  15. S. C. Creagh and R. G. Littlejohn, Phys. Rev. A 44, 836 (1991) S. C. Creagh and R. G. Littlejohn, J. Phys. A 25, 1643 (1992)

    Article  CAS  Google Scholar 

  16. A. M. Ozorio de Almeida and J. H. Hannay, J. Phys. A 20, 5873 (1987) see also A. M. Ozorio de Almeida: Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, Cambridge, 1988)

    Article  Google Scholar 

  17. S. Tomsovic, M. Grinberg, and D. Ullmo, Phys. Rev. Lett. 75, 4346 (1995) D. Ullmo, M. Grinberg, and S. Tomsovic, Phys. Rev. E 54, 135 (1996)

    Article  CAS  Google Scholar 

  18. M. Brack, P. Meier, and K. Tanaka, J. Phys. A 32, 331 (1999)

    Article  CAS  Google Scholar 

  19. M. Hénon and C. Heiles, Astr. J. 69, 73 (1964)

    Article  Google Scholar 

  20. M. Brack, R. K. Bhaduri, J. Law, M. V. N. Murthy, and Ch. Maier, Chaos 5, 317 (1995); Erratum: Chaos 5, 707 (1995)

    Article  Google Scholar 

  21. M. Brack, in: Festschrift in honor of the 75th birthday of Martin Gutzwiller, A. Inomata et al. (Eds.), Foundations of Physics 31, 209 (2001); LANL preprint nlin.CD/0006034

    Google Scholar 

  22. M. Sieber, J. Phys. A 29, 4715 (1996) H. Schomerus and M. Sieber, J. Phys. A 30, 4537 (1997) M. Sieber, J. Phys. A 30, 4563 (1997) M. Sieber and H. Schomerus, J. Phys. A 31, 165 (1998)

    Google Scholar 

  23. M. Kuś, F. Haake, and D. Delande, Phys. Rev. Lett. 71, 2167 (1993)

    Article  Google Scholar 

  24. H. Schomerus, Europhys. Lett. 38, 423 (1997); J. Phys. A 31, 4167 (1998) J. Main and G. Wunner, Phys. Rev. A 55, 1753 (1997) J. Main and G. Wunner, Phys. Rev. E 57, 7325 (1998)

    Article  CAS  Google Scholar 

  25. T. Bartsch, J. Main, and G. Wunner, Ann. Phys. (N. Y.) 277, 19 (1999)

    Article  CAS  Google Scholar 

  26. A. Magner, S. N. Fedotkin, K. Arita, T. Misu, K. Matsuyanagi, T. Schachner, and M. Brack, Prog. Theor. Phys. (Japan) 102, 551 (1999)

    Article  Google Scholar 

  27. A. G. Magner, S. N. Fedotkin, K. Arita, K. Matsuyanagi, and M. Brack, Phys. Rev. A (2001), in press; LANL preprint nlin.SI/0101035 A. G. Magner et al., to be published

    Google Scholar 

  28. S. C. Creagh, Ann. Phys. (N. Y.) 248, 60 (1996)

    Article  CAS  Google Scholar 

  29. D. Ullmo, K. Richter, and R. A. Jalabert, Phys. Rev. Lett. 74, 383 (1995) K. Richter, D. Ullmo, and R. A. Jalabert, Phys. Rep. 276, 1 (1996)

    Article  CAS  Google Scholar 

  30. P. Meier, M. Brack, and S. C. Creagh, Z. Phys. D 41, 281 (1997)

    Article  CAS  Google Scholar 

  31. M. Brack, S. C. Creagh, and J. Law, Phys. Rev. A 57, 788 (1998)

    Article  CAS  Google Scholar 

  32. H. Frisk, Nucl. Phys. A 511, 309 (1990)

    Article  Google Scholar 

  33. K. Arita, A. Sugita, and K. Matsuyanagi, Prog. Theor. Phys. 100, 1223 (1998)

    Article  CAS  Google Scholar 

  34. V. V. Pashkevich, P. Meier, M. Brack, and A. V. Unzhakova, Regensburg preprint TPR-00-24 (2000)

    Google Scholar 

  35. M. Brack and Ch. Amann, in: International Workshop on Fission Dynamics of Atomic Clusters and Nuclei, D. Brink et al. (Eds.) (World Scientific Publishing, Singapore, 2001), in press; LANL preprint nucl-th/0010047

    Google Scholar 

  36. G. Littlejohn and W. G. Flynn, Phys. Rev. A 44, 5239 (1991)

    Article  CAS  Google Scholar 

  37. H. Frisk and T. Guhr, Ann. Phys. (N. Y.) 221, 229 (1993)

    Article  Google Scholar 

  38. J. Bolte and S. Keppeler, Ann. Phys. (N. Y.) 274, 125 (1999) see also J. Bolte, Adv. Solid State Phys. (this volume)

    Article  CAS  Google Scholar 

  39. M. Pletyukhov, M. Mehta, and Ch. Amann, to be published

    Google Scholar 

  40. M. Brack, J. Damgård, A. S. Jensen, H. C. Pauli, V. M. Strutinsky, and C. Y. Wong, Rev. Mod. Phys. 44, 320 (1972)

    Article  CAS  Google Scholar 

  41. M. Brack, S. M. Reimann, and M. Sieber, Phys. Rev. Lett. 79, 1817 (1997)

    Article  CAS  Google Scholar 

  42. M. Brack, P. Meier, S. M. Reimann, and M. Sieber, in: Similarities and differences between atomic nuclei and clusters, Y. Abe et al. (Eds.) (American Institute of Physics, 1998) p. 17

    Google Scholar 

  43. M. Brack, M. Sieber, and S. M. Reimann, in Quantum Chaos Y2K, Proceedings of Nobel Symposium 116, K.-F. Berggren and S. Åberg (Eds.), Physica Scripta Vol. T90 (2001) [4], p. 146

    Google Scholar 

  44. C. Gustafsson, P. Möller, and S. G. Nilsson, Phys. Lett. 34 B, 349 (1971)

    Google Scholar 

  45. C. Gould et al., Phys. Rev. B 51, 11213 (1995)

    Article  CAS  Google Scholar 

  46. G. Kirczenov et al., Phys. Rev. B 56, 7503 (1997)

    Article  Google Scholar 

  47. J. Blaschke and M. Brack, Europhys. Lett. 50, 294 (2000)

    Article  Google Scholar 

  48. J. Blaschke, Ph. D. Thesis, Regensburg University, 1999 available at «http://www.joachim-blaschke.de»

  49. K. Richter, Europhys. Lett. 29, 7 (1995) G. Hackenbroich and F. von Oppen, Europhys. Lett. 29, 151 (1995)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Regensburg, D-93040, Regensburg, Germany

    Matthias Brack

Authors
  1. Matthias Brack
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. I Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355, Hamburg, Germany

    Bernhard Kramer

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Brack, M. (2001). Semiclassical Description of Shell Effects in Finite Fermion Systems. In: Kramer, B. (eds) Advances in Solid State Physics. Advances in Solid State Physics Volume 41, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44946-9_37

Download citation

  • DOI: https://doi.org/10.1007/3-540-44946-9_37

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42000-2

  • Online ISBN: 978-3-540-44946-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation