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Unified approach to quantum fluctuations in tunnelling including dissipation

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Il Nuovo Cimento D

Summary

A simple procedure for evaluating quantum fluctuations at zero temperature has been applied to derive the decay rate for a metastable state in strongly anharmonic potentials (quartic and cubic). We also derive the tunnelling splitting and the energy shift in symmetrical and nearly symmetrical double-well potentials. Dissipation is then considered for the decay of a metastable state, both in the limit of weak and strong damping.

Riassunto

Un metodo semplificato per la valutazione delle fluttuazioni quantistiche, a temperatura zero, è stato impiegato per ottenere la velocità di decadimento di uno stato metastabile in potenziali fortemente anarmonici (quartico e cubico). Si ricavano pure la separazione per tunnelling e lo spostamento di energia nel caso di potenziale a doppio pozzo, simmetrico e quasi simmetrico. Si considerano poi effetti dissipati per il decadimento di uno stato metastabile, sia nel limite di debole che di forte smorzamento.

Резюме

Простая процедура оценки квантовых флуктуаций при нулевой температуре применяется для вывода скорости распада метастабильного состояния в сильно ангармонических потенциалах (четвертого и кубичкского порядков). Мы также выводим расщепление за счет туннелирования и сдвиг энергии в потенциалах симметричной и почти симметричной двойной ямы. Затем рассматривается влияние диссипации при распаде метастабильного состояния в пределе слабого и сильного затухания.

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References

  1. R. P. Feynman, andA. R. Hibbs:Quantum Mechanics and Path Integrals (Mc Graw-Hill, New York, N. Y., 1965).

    MATH  Google Scholar 

  2. S. Coleman, inThe Whys of Subnuclear Physics, edited byA. Zichichi, (Plenum Press, New York, N. Y., 1979), p. 805.

    Google Scholar 

  3. L. S. Schulman:Techniques and Applications of Path Integration (Wiley-Interscience, New York, N. Y., 1981).

    MATH  Google Scholar 

  4. E. Gildener andA. Patrascioiu:Phys. Rev. D,16, 423 (1977).

    Article  Google Scholar 

  5. S. Coleman:Phys. Rev. D,15, 2929 (1977).

    Article  Google Scholar 

  6. C. G. Callan Jr. andS. Coleman:Phys. Rev. D,16, 1762 (1977).

    Article  Google Scholar 

  7. J. P. Sethna:Phys. Rev. B,24, 698 (1981);25, 5050 (1982).

    Article  ADS  Google Scholar 

  8. U. Weiss andW. Haeffner:Phys. Rev. D,27, 2916 (1983).

    Article  ADS  Google Scholar 

  9. U. Weiss:Phys. Rev. A,25, 2444 (1982).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  11. A. O. Caldeira andA. J. Leggett:Phys. Rev.,46, 211 (1981);Ann. Phys. (N.Y.),149, 374 (1983);153, 445 (1984).

    ADS  Google Scholar 

  12. H. Grabert andU. Weiss:Phys. Rev. Lett.,52, 2193 (1984);53, 1787 (1984);54, 1605 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  13. M. P. A. Fisher andA. T. Dorsey:Phys. Rev.,54, 1609 (1985).

    ADS  Google Scholar 

  14. D. Waxman andA. J. Leggett:Phys. Rev. B,32, 4450 (1985).

    Article  ADS  Google Scholar 

  15. D. Mugnai andA. Ranfagni:Phys. Lett. A,109, 219 (1985).

    Article  ADS  Google Scholar 

  16. A. Ranfagni, D. Mugnai andR. Englman: inTunneling, edited byJ. Jortner andB. Pulman (D. Reidel P. C., Dordrecht, 1986), p. 65.

    Google Scholar 

  17. A. Barone andG. Paternò:Physics and Applications of the Josephson Effect (Wiley, New York, N. Y., 1982).

    Google Scholar 

  18. Yu. N. Ovchinnikov, R. Cristiano andA. Barone:J. Appl. Phys.,56, 1473 (1984).

    Article  Google Scholar 

  19. A. Barone, C. Camerlingo andR. Cristiano:Phys. Rev. Lett.,54, 157 (1985).

    Article  ADS  Google Scholar 

  20. H. Grabert: in SQUID ’85Superconducting Quantum Interference Devices, edited byH. D. Hahlbohm andH. Lübbig (de Gruyter, Berlin, 1985).

    Google Scholar 

  21. S. Chakravarty andS. Kivelson:Phys. Rev. B,32, 76 (1985).

    Article  ADS  Google Scholar 

  22. J. M. Martinis, M. H. Devoret andJ. Clarke:Phys. Rev. Lett.,55, 1543 (1985).

    Article  ADS  Google Scholar 

  23. D. B. Schwartz, B. Sen, C. N. Archie andJ. E. Lukens:Phys. Rev. Lett.,55, 1547 (1985).

    Article  ADS  Google Scholar 

  24. L. P. Felsen andN. Marcuvitz:Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chapt. 4.

    Google Scholar 

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

    Article  ADS  Google Scholar 

  26. W. H. Miller:Adv. Chem. Phys.,25, 69 (1974);J. Chem. Phys.,63, 996 (1975);83, 960 (1979).

    Article  Google Scholar 

  27. A. I. Larkin andYu. N. Ovchinnikov:Ž. Ėksp. Teor. Fiz.,86, 719 (1984) (English translation:J. Exp. Teor. Fiz.,59, 420 (1984)).

    Google Scholar 

  28. H. Goldstein:Classical Mechanics (Addison-Wesley, Reading, Mass., 1965), Chapt. 1.

    Google Scholar 

  29. M. Büttiker andR. Landauer:Phys. Rev. Lett.,49, 1739 (1982);IBM J. Res. Dev.,30, 451 (1986).

    Article  ADS  Google Scholar 

  30. A. Ranfagni, D. Mugnai andP. Moretti: inProceedings of the II Soviet-Italian Symposium on Weak Superconductivity, Napoli, Italy, 5–7 May 1987, edited byA. Barone (World Scientific, in press).

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Authors and Affiliations

  1. Istituto di Ricerca sulle Onde Elettromagnetiche del C.N.R., Frienze, Italia

    A. Ranfagni & D. Mugnai

  2. Soreq Nuclear Research Center, Yavne, Israel

    R. Englman

Authors
  1. A. Ranfagni
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  2. D. Mugnai
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  3. R. Englman
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Ranfagni, A., Mugnai, D. & Englman, R. Unified approach to quantum fluctuations in tunnelling including dissipation. Nouv Cim D 9, 1009–1032 (1987). https://doi.org/10.1007/BF02464853

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  • DOI: https://doi.org/10.1007/BF02464853

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