Skip to main content

Trajectories of Particles Interacting with Environments

  • Chapter
Waves and Particles in Light and Matter
  • 289 Accesses

Abstract

We discuss the behaviour of open quantum systems, quantum objects coupled to environments, in the Schrödinger picture. The object state evolves in a non-linear and stochastic manner. We illustrate this for a frictional environment by calculating the de Broglie-Bohm trajectories for some simple examples.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. de Broglie, in Rapport au Ve Congres de Physique Solvay (Gauthier-Villars, Paris, 1930).

    Google Scholar 

  2. D. Bohm, Phys. Rev. 85, 166; 180 (1952).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. D. Bohm, B. J. Hiley, and P. N. Kaloyerou, Phys. Rep. 144, 321 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  4. D. Bohm, J. Bub, Rev. Mod. Phys. 38, 453 (1966).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. P. Pearle, Phys. Rev. D 13, 857 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  6. P. Pearle, Int. J. Theor. Phys. 18 489 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Pearle, J. Stat. Phys. 41, 719 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  8. N. Gisin, Phys. Rev. Lett. 52, 1657 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  9. N. Gisin, Helv. Phys. Acta 62, 363 (1989).

    MathSciNet  Google Scholar 

  10. L. Diósi, J. Phys. A 21, 2885 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. L. Diósi, Phys. Lett. A 129, 419 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  12. G.-C. Ghirardi, A. Rimini, and T. Weber Phys. Rev. D 34, 470 (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. G.-C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  14. N. Gisin, I. C. Percival, J. Phys. A 25, 5677 (1992).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. For an interesting discussion of this point, see Ref. 14.

    Google Scholar 

  16. G. W. Ford, M. Kac, and P. Mazur, J. Math. Phys. 6, 504 (1965).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Lett. A 128, 29 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  18. M. D. Kostin, J. Chem. Phys. 57, 3589 (1972).

    Article  ADS  Google Scholar 

  19. M. D. Kostin, J. Stat. Phys. 12, 145 (1975).

    Article  ADS  Google Scholar 

  20. T. P. Spiller, P. S. Spencer, T. D. Clark, J. F. Ralph, H. Prance, R. J. Prance, and A. J. Clippingdale, Found. Phys. Lett. 4, 507 (1991).

    Article  MathSciNet  Google Scholar 

  21. H. Nyquist, Phys. Rev. 32, 110 (1928).

    Article  ADS  Google Scholar 

  22. H. B. Callen, J. H. Welton, Phys. Rev. 83, 34 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. R. Kubo, J. Phys. Soc. Japan 12, 570 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  24. R. P. Feynman, F. L. Vernon Jr., Ann. Phys. 24, 118 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  25. K. K. Kan, J. J. Griffin, Phys. Lett. 50B, 241 (1974).

    ADS  Google Scholar 

  26. N. Gisin, J. Phys. A 14, 2259 (1981).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. C. Dewdney, and M. M. Lam, in Information Dynamics

    Google Scholar 

  28. H. Atmanspacher and H. Scheingraber, eds. (NATO ASI Series B 256) (Plenum, New York, 1991), p. 329.

    Google Scholar 

  29. C. Dewdney, G. Horton, M. M. Lam, Z. Malik, and M. Schmidt, Found. Phys. 22, 1217 (1992).

    Article  MathSciNet  ADS  Google Scholar 

  30. C. Philippidis, C. Dewdney, and B. J. Hiley, Nuovo Cimento 52B, 15 (1979).

    MathSciNet  ADS  Google Scholar 

  31. C. Dewdney, and B. J. Hiley, Found. Phys. 12, 27 (1982).

    Article  ADS  Google Scholar 

  32. T. P. Spiller, T. D. Clark, R. J. Prance, H. Prance, and D. A. Poulton Found. Phys. Lett. 4, 19 (1991).

    Article  Google Scholar 

  33. For a recent review, see T. P. Spiller, T. D. Clark, R. J. Prance, and A. Widom, Prog. Low Temp. Phys. XIII, 219 (1992).

    Article  Google Scholar 

  34. A. O. Caldeira, and A. J. Leggett, Phys. Rev. Lett. 46, 211 (1981).

    Article  ADS  Google Scholar 

  35. A. O. Caldeira, and A. J. Leggett, Ann. Phys. 149, 374 (1983).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Spiller, T.P. (1994). Trajectories of Particles Interacting with Environments. In: van der Merwe, A., Garuccio, A. (eds) Waves and Particles in Light and Matter. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2550-9_38

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-2550-9_38

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6088-9

  • Online ISBN: 978-1-4615-2550-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics