Skip to main content
SpringerLink
Log in

Thermal enhancement of the quantum decay rate in a dissipative system

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The quantum decay of a metastable system which interacts with an environment at temperatureT is considered. A general formula for the decay rate at finite temperatures is obtained by a method which is based on the framework recently described by Caldeira and Leggett. The thermal enhancement of the tunnelling rate at low temperatures is discussed for arbitrary metastable potentials, and it is found that the exponent of the rate obeys a power law in a dissipative system. The power law exponent is shown to be a characteristic feature of the dissipative mechanism. Finally, a universally valid formula for the thermal enhancement factor is given, where the form of the potential enters only through the frequency of small oscillations about the metastable minimum and the “length” of the zero temperature bounce trajectory.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Boer, W. den, Bruyn Ouboter, R. de: Physica98B, 185 (1980)

    Google Scholar 

  2. Prance, R.J., et al.: Nature (London)289, 543 (1981)

    Article  Google Scholar 

  3. Voss, R.F., Webb, R.A.: Phys. Rev. Lett.47, 265 (1981)

    Article  Google Scholar 

  4. Jackel, L.D., et al.: Phys. Rev. Lett.47, 697 (1981)

    Article  Google Scholar 

  5. Bol, D.W., Weelderen, R. van, Bruyn Ouboter, R. de: Physica122B, 1 (1983)

    Google Scholar 

  6. Caldeira, A.O., Leggett, A.J.: Phys. Rev. Lett.46, 211 (1981)

    Article  Google Scholar 

  7. Schmid, A.: J. Low Temp. Phys.49, 609 (1982)

    Article  Google Scholar 

  8. Ambegaokar, V., Eckern, U., Schön, G.: Phys. Rev. Lett.48, 1745 (1982)

    Article  Google Scholar 

  9. Zwerger, W.: Z. Phys. B — Condensed Matter47, 129 (1982)

    Article  Google Scholar 

  10. Chakravarty, S.: Phys. Rev. Lett.49, 681 (1982)

    Article  Google Scholar 

  11. Bray, A.J., Moore, M.A.: Phys. Rev. Lett.49, 1546 (1982)

    Article  Google Scholar 

  12. Kurkijärvi, J.: Phys. Lett.88A, 241 (1982)

    Google Scholar 

  13. Büttiker, M., Landauer, R.: Phys. Rev. Lett.49, 1739 (1983)

    Article  Google Scholar 

  14. Zwerger, W.: Z. Phys. B — Condensed Matter51, 301 (1983)

    Article  Google Scholar 

  15. Caldeira, A.O., Leggett, A.J.: Ann. Phys. (NY)149, 374 (1983)

    Article  Google Scholar 

  16. Larkin, A.I., Ovchinnikov, Yu.N.: JEPT Lett.37, 382 (1983)

    Google Scholar 

  17. Harris, R.A., Silbey, R.: J. Chem. Phys.78, 7330 (1983)

    Article  Google Scholar 

  18. Chakravarty, S., Leggett, A.J.: Phys. Rev. Lett.52, 5 (1984)

    Article  Google Scholar 

  19. Affleck, I.K.: Phys. Rev. Lett.46, 388 (1981)

    Article  Google Scholar 

  20. Weiss, U., Häffner, W.: Phys. Rev. D27, 2916 (1983)

    Article  Google Scholar 

  21. Grabert, H., Weiss, U., Hänggi, P.: Phys. Rev. Lett.52, 2193 (1984)

    Article  Google Scholar 

  22. Langer, J.S.: Ann. Phys. (NY)41, 108 (1967)

    Article  Google Scholar 

  23. Coleman, S.: Phys. Rev. D15, 2929 (1977)

    Article  Google Scholar 

  24. Callan, C.G., Coleman, S.: Phys. Rev. D16, 1762 (1977)

    Article  Google Scholar 

  25. Stone, M.: Phys. Lett. B67, 186 (1977)

    Article  Google Scholar 

  26. Feynman, R.P., Vernon, F.L.: Ann. Phys. (NY)24, 118 (1963)

    Article  Google Scholar 

  27. Feynman, R.P., Hibbs, A.R.: Quantum mechanics and path integrals. New York: Mc Graw-Hill 1965

    Google Scholar 

  28. Chang, L.D., Chakravarty, S.: Phys. Rev. B29, 130 (1984)

    Article  Google Scholar 

  29. Kurkijärvi, J.: Phys. Rev. B6, 832 (1972)

    Article  Google Scholar 

  30. Green, M.S.: J. Chem. Phys.20, 1281 (1952)

    Article  Google Scholar 

  31. Kubo, R.: Rep. Prog. Phys. (London)29, 255 (1966)

    Article  Google Scholar 

  32. Grabert, H.: Springer Tracts in Modern Physics. Vol. 95, Chap. 7. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  33. Zwanzig, R.: J. Stat. Phys.9, 215 (1973)

    Article  Google Scholar 

  34. Grabert, H., Weiss, U., Talkner, P.: Z. Phys. B — Condensed Matter55, 87 (1984)

    Article  Google Scholar 

  35. Feynman, R.P.: Statistical mechanics. New York: Benjamin 1972

    Google Scholar 

  36. Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions, p. 258f. New York: Dover 1972

    Google Scholar 

  37. Narayanamurti, V., Pohl, R.O.: Rev. Mod. Phys.42, 201 (1970) (1970)

    Article  Google Scholar 

  38. Bridges, F.: CRC Crit. Rev. Solid State Sci.5, 1 (1975)

    Google Scholar 

  39. Sethna, J.P.: Phys. Rev. B25, 5050 (1982)

    Article  Google Scholar 

  40. Ref. 36. p. 17

    Google Scholar 

  41. Ref. 36 p. 806, 886

    Google Scholar 

  42. Grabert, H., Weiss, U.: Preprint (1984)

  43. Weiss, U., Riseborough, P., Hanggi, P., Grabert, H.: Phys. Lett. A (in press)

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80, Germany

    Hermann Grabert & Ulrich Weiss

Authors
  1. Hermann Grabert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ulrich Weiss
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grabert, H., Weiss, U. Thermal enhancement of the quantum decay rate in a dissipative system. Z. Physik B - Condensed Matter 56, 171–183 (1984). https://doi.org/10.1007/BF01469699

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01469699

Keywords

Search

Navigation