Skip to main content
Log in

Dynamical origin of the quantum Zeno effect

  • Part II. Invited Papers Dedicated to Mikio Namiki
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The quantum Zeno effect is often studied and understood in term of nonunitary evolutions, involving projections à la von Neumann (measurements). We propose a dynamical explanation of this effect, which involves only unitary operators. The limit of infinitely frequent measurements is critically discussed: it is unphysical, yet interesting and peculiar.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Inagaki, M. Namiki, and T. Tajiri,Phys. Lett. A. 166, 5 (1992).

    Article  ADS  Google Scholar 

  2. A. Beskow and J. Nilsson,Ark. Fys. 34, 561 (1967).

    Google Scholar 

  3. L. A. Khaltin,Zh. Eksp. Teor. Fiz. Pis. Red. 8, 106 (1968) [JETP Lett 8, 65 (1968)];Phys. Lett. B 112, 223 (1982);Usp. Fiz. Nauk 160, 185 (1990) [Sov. Phys. Usp. 33, 10 (1990)].

    Google Scholar 

  4. L. Fonda, G. C. Ghirardi, A. Rimini, and T. Weber,Nuovo Cimento A 15, 689 (1973);18 805 (1973). A. DeGasperis, L. Fonda, and G. C. Ghirardi,Nuovo Cimento A 21, 471 (1974).

    Article  ADS  Google Scholar 

  5. B. Misra and E. C. G. Sudarshan.J. Math. Phys. 18 756 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  6. R. J. Cook,Phys. Scr. T 21, 49 (1988).

    ADS  Google Scholar 

  7. W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland,Phys. Rev. A,41, 2295 (1990).

    Article  ADS  Google Scholar 

  8. T. Petrosky, S. Tasaki, and I. Prigogine,Phys. Lett. A 151, 109 (1990);Physica A 170, 306 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Peres and A. Ron,Phys. Rev. A 42, 5720 (1990); L. E. Ballentine,Phys. Rev. A 43, 5165 (1991); W. H. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland,Phys. Rev. A 43 5168 (1991). V. Frerichs and A. Schenzle, inFoundations of Quantum Mechanics, T. D. Black, M. M. Nieto, H. S. Pilloff, M. O. Scully, and R. M. Sinclair, eds. (World Scientific, Singapore, 1992). D. Home and M. A. B. Whitaker,J. Phys. A 25, 657 (1992);Phys. Lett. A 173, 327 (1993). R. Onofrio, C. Presilla, and U. Tambini,Phys. Lett A 183, 135 (1993). Ph. Blanchard and A. Jadezyk,Phys. Lett. A 183, 272 (1993); T. P. Altenmuller and A. Schenzle,Phys. Rev. A 49, 2016 (1994). M. Berry, inFundamental Problems in Quantum Theory, D. M. Greenberger and A. Zeilinger, eds. (Ann. N. Y. Acad. Sci. 755, New York, 1995), p. 303. A. Beige and G. Hegerfeldt,Phys. Rev. A 53, 53 (1996).

    Article  ADS  Google Scholar 

  10. S. Pascazio, M. Namiki, G. Badurek, and H. Rauch,Phys. Lett. A 179, 155 (1993).

    Article  ADS  Google Scholar 

  11. S. Pascazio and M. Namiki,Phys. Rev. A 50, 4582 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Namiki and N. Mugibayashi,Prog. Theor. Phys.,10, 474 (1953).

    Article  ADS  MATH  Google Scholar 

  13. J. von Neumann,Die Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932); English translation by E. T. Beyer:Mathematical Foundations of Quantum Mechanics, (Princeton University Press, Princeton, 1955).

    Google Scholar 

  14. S. Machida and M. Namiki,Prog. Theor. Phys 63, 1457, 1833 (1980). M. Namiki,Found. Phys. 18, 29 (1988).

    Article  ADS  Google Scholar 

  15. M. Namiki and S. Pascazio,Phys. Rev. A 44, 39 (1991).Phys. Rep. 232, 301 (1993). M. Namiki, S. Pascazio, and C. Schiller,Phys. Lett. A 182, 17 (1994).

    Article  ADS  Google Scholar 

  16. A. Peres,Am. J. Phys. 48, 931 (1980);Ann. Phys. 129, 33 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  17. D. Home and M. A. B. Whitaker,J. Phys. A 25, 657 (1992).

    Article  ADS  Google Scholar 

  18. G. Gamow,Z. Phys. 51, 204 (1928).

    Article  ADS  Google Scholar 

  19. V. Weisskopf and E. P. Wigner,Z. Phys. 63, 54 (1930);65, 18 (1930).

    Article  ADS  Google Scholar 

  20. G. Breit and E. P. Wigner,Phys. Rev. 49, 519 (1936).

    Article  ADS  MATH  Google Scholar 

  21. E. Fermi,Nuclear Physics (University of Chicago Press, Chicago, 1950), pp. 136, 148; see alsoNotes on Quantum Mechanics. A Course Given at the University of Chicago in 1954, E. Segré, ed. (University of Chicago Press, Chicago, 1960), Lecture 23; alsoRev. Mod. Phys. 4, 87 (1932).

    MATH  Google Scholar 

  22. L. Mandelstam and I. Tamm,J. Phys. 9, 249 (1945). V. Fock and N. Krylov,J. Phys. 11, 112 (1947).

    MathSciNet  Google Scholar 

  23. E. J. Hellund,Phys. Rev. 89, 919 (1953).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. L. A. Khalfin,Dokl. Akad. Nauk SSSR 115 277 (1957). [Sov. Phys. Dokl.,2, 340 (1957)];Zh. Eksp. Teor. Fiz. 33, 1371 (1958) [Sov. Phys. JETP 6, 1053 (1958)].

    Google Scholar 

  25. R. E. A. C. Paley and N. Wiener,Fourier Transforms in the Complex Domain (American Mathematical Society, Colloquium Publications, Vol. XIX, New York, 1934).

  26. L. Fonda, G. C. Ghirardi, and A. Rimini,Rep. Prog. Phys. 41, 587 (1978). P. Exner,Open Quantum Systems and Feynman Integrals (Reidel, Dordrecht, 1985); see in particular Chap. I (the notes to Sec. 1.5 are very interesting). G-C Cho, H. Kasari, and Y. Yamaguchi,Prog. Theor. Phys. 90, 803 (1993). L. P. Horwitz,Found. Phys.25, 39 (1995).

    Article  ADS  Google Scholar 

  27. H. Nakazato, M. Namiki, and S. Pascazio,Int. J. Mod. Phys. B 10, 247 (1996).

    Article  ADS  Google Scholar 

  28. Ref. 13 p. 195 (p. 366 in English translation).

    Google Scholar 

  29. G. C. Ghirardi, C. Omero, T. Weber, and A. Rimini,Nuovo Cimento A 52, 421 (1979). H. Nakazato, M. Namiki, S. Pascazio, and H. Rauch,Phys. Lett. A 199, 27 (1995). A. Venugopalan and R. Ghosh,Phys. Lett A 204, 11 (1995), A. Pati,Phys. Lett. A 215, 7 (1996).

    ADS  Google Scholar 

  30. E. P. Wigner,Am. J. Phys. 31, 6 (1963).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. H. Nakazato, M. Namiki, S. Pascazio, and H. Rauch,Phys. Lett. A 217, 203 (1996).

    Article  ADS  Google Scholar 

  32. B. Gaveau and L. S. Schulman,J. Stat. Phys. 58, 1209 (1990);J. Phys. A 28, 7359 (1995). L. S. Schulman, A. Ranfagni, and D. Mugnai,Phys. Scr. 49, 536 (1994).

    Article  MathSciNet  ADS  Google Scholar 

  33. E. Mihokova, S. Pascazio, and L. S. Schulman,Phys. Rev. A 56, 25 (1997).

    Article  ADS  Google Scholar 

  34. C. Bernardini, L. Maiani, and M. Testa,Phys. Rev. Lett. 71, 2687 (1993).

    Article  ADS  Google Scholar 

  35. P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. Kasevich, inFundamental Problems in Quantum Theory, D. M. Greenberger and A. Zeilinger, eds. (Ann. N.Y. Acad. Sci. 755, New York 1995), p. 383;Phys. Rev. Lett. 74, 4763 (1995).

  36. M. L. Goldberger and F. Seitz,Phys. Rev. 71, 294 (1974).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pascazio, S. Dynamical origin of the quantum Zeno effect. Found Phys 27, 1655–1670 (1997). https://doi.org/10.1007/BF02551443

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02551443

Keywords

Navigation