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The Role of Dissipation in Quantum Tunneling

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Tunneling

Part of the book series: The Jerusalem Symposia on Quantum Chemistry and Biochemistry ((JSQC,volume 19))

Abstract

The rate of kinetic processes hindered by a potential barrier is studied in the temperature range where quantum effects are important. Based on a generalized quantum-mechanical version of Kramer’s Brownian motion approach, a rate theory accounting for thermally activated and tunneling events is presented. The temperature dependence of the rate is studied and the crossover from the Arrhenius law valid at high temperatures to quantum rate theory valid at low temperatures is discussed. The role of memory friction caused by the dissipative coupling to the environment is emphasized.

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References

  1. R. DiFoggio and R. Gomer, Phys. Rev. B25, 3490 (1982)

    Google Scholar 

  2. H. Frauenfelder, in Tunnelling in Biological Systems, edited by B. Chance et al. ( Academic, New York, 1979 )

    Google Scholar 

  3. S. Washburn and R. A. Webb, in New Techniques and Ideas in Quantum Measurement Theory, Ann.N.Y.Ac.Sci. (in press) and references therein

    Google Scholar 

  4. W. Riehemann and E. Nembach, J.Appl.Phys. 55, 1081 (1984)

    Article  CAS  Google Scholar 

  5. H. A. Kramers, Physica (Utrecht) 7, 284 (1940)

    Article  CAS  Google Scholar 

  6. For a recent discussion and a detailed list of references see P. Hanggi, J.Stat.Phys. 42, 105 (1986)

    Google Scholar 

  7. I. K. Affleck, Phys.Rev.Lett. 40, 388 (1981)

    Article  Google Scholar 

  8. V. I. Gol’danskii, Dokl.Akad.Nauk SSSR 124, 1261

    Google Scholar 

  9. V. I. Gol’danskii, Dokl.Akad.Nauk SSSR 127, 1037 (1959)

    Google Scholar 

  10. A. O. Caldeira and A. J. Leggett, Ann.Phys.(N.Y.) 149, 374 (1983)

    Google Scholar 

  11. H. Grabert, U. Weiss, and P. Hanggi, Phys.Rev.Lett. 52, 2193 (1984)

    Article  Google Scholar 

  12. P. Hanggi, H. Grabert, G. -L. Ingold, and U. Weiss, Phys.Rev.Lett. 55, 761 (1985)

    Article  CAS  Google Scholar 

  13. R. F. Grote and J. T. Hynes, J.Chem.Phys. 73, 2715 (1980)

    Article  CAS  Google Scholar 

  14. P. Hanggi and F. Mojtabai, Phys.Rev. A26, 1168 (1982)

    Google Scholar 

  15. B. Carmeli and A. Nitzan, Phys.Rev. A29, 1481 (1984)

    Google Scholar 

  16. H. Grabert and U. Weiss, Z.Phys. B56, 171 (1984)

    Article  Google Scholar 

  17. D. Esteve, M. H. Devoret, and J. M. Martinis, Phys.Rev.B (in press)

    Google Scholar 

  18. H. Grabert and U. Weiss, Phys.Rev.Lett. 53, 1787 (1984)

    Article  Google Scholar 

  19. J. S. Langer, Ann.Phys.(N.Y.) 41, 108 (1967)

    Article  CAS  Google Scholar 

  20. P. G. Wolynes, Phys.Rev.Lett. 47, 968 (1981)

    Article  CAS  Google Scholar 

  21. R. P. Feynman, Statistical Mechanics (Benjamin, New York, 1972 )

    Google Scholar 

  22. A. I. Larkin and Yu. N. Ovchinnikov, Sov.Phys.JETP 59, 420 (1984)

    Google Scholar 

  23. H. Grabert, P. Olschowski, and U. Weiss, Phys.Rev. B32, 3348 (1985)

    Google Scholar 

  24. A.J.Leggett, in Percolation, Localization, and Superconductivity, NATO Advanced Studies Institute, Vol. 109 (eds. A.M.Goldman and S.A.Wolf) ( Plenum, New York, 1984 )

    Google Scholar 

  25. H.Grabert in SQUID’85 (eds. H.D.Hahlbohm and H.Lübbig) (de Gruyter, Berlin, 1985 )

    Google Scholar 

  26. M. Büttiker, E. P. Harris, and R. Landauer, Phys.Rev. B28, 1268 (1983)

    Google Scholar 

  27. H. Risken and K. Voigtländer, J.Stat.Phys. 41, 825 (1985)

    Article  Google Scholar 

  28. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger, preprint

    Google Scholar 

  29. U. Weiss and H. Grabert, Phys.Lett. 108A, 63, (1985)

    Google Scholar 

  30. R. P. Feynman and F. L. Vernon, Ann.Phys.(N.Y.) 24, 118 (1963).

    Article  Google Scholar 

  31. H. Grabert and U. Weiss, Phys.Rev.Lett. 54, 1605 (1985)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Stuttgart, D 7000, Stuttgart 80, Federal Republic of Germany

    Hermann Grabert

Authors
  1. Hermann Grabert
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Tel-Aviv, Israel

    Joshua Jortner

  2. Institut de Biologie Physico-Chimique, Fondation Edmond de Rothschild, Paris, France

    Bernard Pullman

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© 1986 D. Reidel Publishing Company

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Grabert, H. (1986). The Role of Dissipation in Quantum Tunneling. In: Jortner, J., Pullman, B. (eds) Tunneling. The Jerusalem Symposia on Quantum Chemistry and Biochemistry, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4752-8_13

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  • DOI: https://doi.org/10.1007/978-94-009-4752-8_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8611-0

  • Online ISBN: 978-94-009-4752-8

  • eBook Packages: Springer Book Archive

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