Dissipative quantum tunneling

  • Hermann Grabert
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 268)


Recent theoretical predictions on the influence of dissipation and temperature on quantum mechanical tunneling are presented. Based on a generalized quantum mechanical version of Kramers' Brownian motion approach the rate of transitions out of a metastable well is determined. 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. Special attention is given to the phenomenon of macroscopic quantum tunneling in Josephson systems.


Partition Function Zero Mode Josephson Junction Quantum Tunneling Crossover Region 
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  1. [1]
    H.A.Kramers, Physics (Utrecht) 7,284 (1940)Google Scholar
  2. [2]
    V.Narayanamurti and R.O.Pohl, Rev.Mod.Phys.42,201 (1970)Google Scholar
  3. [2a]
    A.Seeger and H.Teichler, in La Diffusion dans les Milieux Condensés-Théories et Applications (Saclay: INSTN, 1976)Google Scholar
  4. [2b]
    J.P.Sethna, Phys.Rev. B24,698 (1981); B25,5050(1982)Google Scholar
  5. [2c]
    Y.Fukai, H.Sugimoto, Adv.Phys. 34,263 (1985)Google Scholar
  6. [3]
    V.I.Gol'danskii, Chemica Scripta (Sweden) 13,1 (1978–79)Google Scholar
  7. [3a]
    R.P.Bell, The Tunnel Effect in Chemistry (Chapman and Hall, London, 1980)Google Scholar
  8. [4]
    H.Frauenfelder, in Tunnelling in Biological Systems, (ed. B.Chance et al.) (Academic, New York, 1979)Google Scholar
  9. [5]
    A.J.Leggett, Progr.Theor.Phys.Suppl. 69,80 (1980)Google Scholar
  10. [5a]
    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
  11. [6]
    R.F.Voss, R.A.Webb, Phys.Rev.Lett. 47,265 (1981)Google Scholar
  12. [6a]
    L.D.Jackel et al., Phys.Rev.Lett.47,697 (1981)Google Scholar
  13. [7]
    S.Washburn, R.A.Webb, R.F.Voss, and S.M.Faris, Phys.Rev.Lett.54,2712 (1985)PubMedGoogle Scholar
  14. [8]
    D.B.Schwartz, B.Sen, C.N.Archie, and J.E.Lukens, Phys.Rev.Lett. 55,1547 (1985)PubMedGoogle Scholar
  15. [9]
    W.den Boer, Bruyn Ouboter, Physica 98B,85 (1980)Google Scholar
  16. [9a]
    R.J.Prance et al., Nature 289,543 (1981)Google Scholar
  17. [10]
    J.M.Martinis, M.H.Devoret, and J.Clarke, Phys.Rev.Lett. 55,1543 (1985)PubMedGoogle Scholar
  18. [10a]
    M.H.Devoret, J.M.Martinis, and J.Clarke, Phys.Rev.Lett. 55,1908 (1985)PubMedGoogle Scholar
  19. [11]
    A.Barone, G.Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982)Google Scholar
  20. [12]
    I.K.Affleck, Phys.Rev.Lett. 46,388 (1981)Google Scholar
  21. [13]
    V.I.Gol'danskii, Dokl.Akad.Nauk SSSR 124,1261; 127,1037(1959)Google Scholar
  22. [14]
    A.O.Caldeira and A.J.Leggett, Phys.Rev.Lett. 46,211( (1981); and: Ann.Phys.(N.Y.)149,374(1983)Google Scholar
  23. [15]
    H.Grabert, U.Weiss, and P.Hanggi, Phys.Rev.Lett. 52,2193 (1984)Google Scholar
  24. [15a]
    H.Grabert and U.Weiss, Z.Phys. B56,171 (1984)Google Scholar
  25. [16]
    H.Grabert and U.Weiss, Phys.Rev.Lett. 53,1787 (1984)Google Scholar
  26. [17]
    J.S.Langer, Ann.Phys.(N.Y.)41,108 (1967)Google Scholar
  27. [18]
    S.Coleman, in The Whys of Subnuclear Physics (ed.A.Zichichi) (Plenum, New York, 1979)Google Scholar
  28. [19]
    A.Schmid, preprintGoogle Scholar
  29. [20]
    P.G.Wolynes, Phys.Rev.Lett. 47,968 (1981)Google Scholar
  30. [20a]
    V.I.Mel'nikov, Zh.Eksp.Teor.Fiz. 87,663 (1984) (Sov.Phys.JETP 60,380(1984))Google Scholar
  31. [20b]
    A.I.Larkin and Yu.N.Ovehinnikov, J.Stat.Phys.41,425 (1985)Google Scholar
  32. [21]
    A.I.Larkin, Yu.N.Ovchinikov, Zh.Eksp.Theor.Fiz.86,719 (1984) (Sov.Phys.JEPT 59,420(1984))Google Scholar
  33. [22]
    L.D.Chang and S.Chakravarty, Phys.Rev. B29,103 (1984); B30,1566(1984)(E)Google Scholar
  34. [23]
    P.Riseborough, P.Hanggi, and E.Freidkin, Phys.Rev.A32,489 (1985)Google Scholar
  35. [23a]
    P.Hanggi, J.Stat.Phys.42,105 (1986)Google Scholar
  36. [24]
    H.Grabert, P.Olschowski, and U.Weiss, Phys.Rev.B32,3348 (1985)Google Scholar
  37. [24a]
    H.Grabert in SQUID'85 (eds. H.D.Hahlbohm and H.Lübbig) (de Gruyter, Berlin, 1985)Google Scholar
  38. [25]
    R.P.Feynman, Statistical Mechanics (Benjamin, New York, 1972)Google Scholar
  39. [25b]
    R.P.Feynman and F.L.Vernon, Ann.Phys.(N.Y.) 24,118 (1963)Google Scholar
  40. [26]
    A.J.Leggett, Phys.Rev.B30,1208 (1984)Google Scholar
  41. [26a]
    D.Estève, M.H.Devoret, and J.M.Martinis, Phys.Rev.B(in press)Google Scholar
  42. [27]
    R.F.Grote and J.T.Hynes, J.Chem.Phys.73,2715 (1980)Google Scholar
  43. [27a]
    P.Hanggi and F.Mojtabai, Phys.Rev.A26,1168 (1982)Google Scholar
  44. [27b]
    B.Carmeli and A.Nitzan, Phys.Rev.A29,1481 (1984)Google Scholar
  45. [28]
    P.Hanggi, H.Grabert, G.-L.Ingold, and U.Weiss, Phys.Rev.Lett. 55,761 (1985)PubMedGoogle Scholar
  46. [29]
    C.G.Callen and S.Coleman, Phys.Rev.D16,1762 (1977)Google Scholar
  47. [30]
    H.Grabert, P.Olschowski, and U.Weiss, unpublishedGoogle Scholar
  48. [31]
    M.Büttiker, E.P.Harris, and R.Landauer, Phys.Rev.B28,1268 (1983)Google Scholar
  49. [31a]
    H.Risken and K.Voigtländer, J.Stat.Phys.41,825 (1985)Google Scholar
  50. [32]
    E.Ben-Jacob and Y.Gefen, Phys.Lett.108A,289 (1985)Google Scholar
  51. [32a]
    K.K.Likharev and A.B.Zorin, J.Low Temp.Phys.59,347 (1985)Google Scholar
  52. [32b]
    F.Guinea and G.Schön, Europhys.Lett.1,585 (1986)Google Scholar
  53. [33]
    M.H.Devoret, J.M.Martinis, D.Estève, and J.Clarke, Phys.Rev.Lett. 53,1260 (1984)Google Scholar
  54. [34]
    S.Chakravarty and A.J.Leggett,Phys.Rev.Lett.53,5 (1984)CrossRefGoogle Scholar
  55. [34a]
    H.Grabert and U.Weiss, Phys.Rev.Lett.54,1605 (1985)CrossRefPubMedGoogle Scholar
  56. [34b]
    A.J.Leggett, S.Chakravarty, A.T.Dorsey, M.P.A.Fisher, A.Garg and W.Zwerger, preprintGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Hermann Grabert
    • 1
  1. 1.Service de Physique et de Résonance MagnétiqueCentre d'Etudes Nucleaires de SaclayGif sur Yvette CedexFrance

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