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Bohmian Trajectories Post-Decoherence

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Abstract

The role of the environment in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. One of the effects of the interaction is to produce a rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is initially in an approximate energy eigenstate, then there is a tendency for the Bohmian trajectory to become approximately classical on a longer time-scale. The relationship between this phenomenon and the behaviour of the Wigner function post-decoherence is discussed.

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REFERENCES

  1. D. Bohm and B. J. Hiley, The Undivided Universe (Routledge, London, 1993).

    Google Scholar 

  2. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

    Google Scholar 

  3. P. R. Holland, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing, A Fine and S. Goldstein, eds. (Kluwer Academic, Dordrecht, 1996).

    Google Scholar 

  4. D. M. Appleby, Found. Phys. 29, 1863 (1999).

    Google Scholar 

  5. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984).

    Google Scholar 

  6. M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics of Information, W. H. Zurck, ed. (Addison-Wesley, Reading, 1990).

    Google Scholar 

  7. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).

    Google Scholar 

  8. R. Omnés, The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, 1994).

    Google Scholar 

  9. W. H. Zurek, Phys. Today 40, October 36 (1991).

    Google Scholar 

  10. W. H. Zurek, Prog. Theor. Phys. 89, 281 (1993).

    Google Scholar 

  11. W. H. Zurek, Phil. Trans. Roy. Soc. Lond. A 356, 1793 (1998).

    Google Scholar 

  12. E. Joos and H. D. Zeh, Z. Phys. B 59, 223 (1985).

    Google Scholar 

  13. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996).

    Google Scholar 

  14. W. M. Dickson, Quantum Chance and non-Locality (Cambridge University Press, Cambridge, 1998).

    Google Scholar 

  15. H. D. Zeh, Los Alamos e-print, xxx.lanl.gov, quant-ph/9812059.

  16. A. O. Caldeira and A. J. Leggett, Physica A 121, 587 (1983).

    Google Scholar 

  17. H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rep. 168, 115 (1988).

    Google Scholar 

  18. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992).

    Google Scholar 

  19. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 47, 1576 (1993).

    Google Scholar 

  20. L. P. Hughston, R. Josza, and W. K. Wootters, Phys. Lett. A 183, 14 (1993).

    Google Scholar 

  21. J. J. Halliwell and A. Zoupas, Phys. Rev. D 55, 4697 (1997).

    Google Scholar 

  22. J. J. Halliwell and T. Yu, Phys. Rev. D 53, 2012 (1996).

    Google Scholar 

  23. J. Anglin and S. Habib, Mod. Phys. Lett. A 11, 2655 (1996).

    Google Scholar 

  24. L. Diosi, Europhys. Lett. 22, 1 (1993).

    Google Scholar 

  25. L. Diosi, Physica A 199, 517 (1993).

    Google Scholar 

  26. M. Tegmark, Found. Phys. Lett. 6, 571 (1993).

    Google Scholar 

  27. J. Kupsch, Los Alamos e-print, xxx.lanl.gov, quant-ph/9811010.

  28. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).

    Google Scholar 

  29. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).

    Google Scholar 

  30. C. Anastopoulos and J. J. Halliwell, Phys. Rev. D 51, 6870 (1995).

    Google Scholar 

  31. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940).

    Google Scholar 

  32. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).

    Google Scholar 

  33. H. W. Lee, Phys. Rep. 259, 147 (1995).

    Google Scholar 

  34. U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, Cambridge, 1997).

    Google Scholar 

  35. R. J. Glauber, Phys. Rev. Lett. 10, 84 (1963).

    Google Scholar 

  36. E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).

    Google Scholar 

  37. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1980).

    Google Scholar 

  38. H. Geiger, G. Obermair, and Ch. Helm, Los Alamos e-print, xxx.lanl.gov, quant-ph/9906082.

  39. J. J. Halliwell, Los Alamos e-print, xxx.lanl.gov, quant-ph/9902008.

  40. E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, N.J., 1985).

    Google Scholar 

  41. R. I. Sutherland, Found. Phys. 27, 845 (1997).

    Google Scholar 

  42. P. R. Holland, Found. Phys. 28, 881 (1998).

    Google Scholar 

  43. E. Deotto and G. C. Ghirardi, Found. Phys. 28, 1 (1998).

    Google Scholar 

  44. S. M. Roy and V. Singh, Los Alamos e-print, quant-ph/9811041.

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Appleby, D.M. Bohmian Trajectories Post-Decoherence. Foundations of Physics 29, 1885–1916 (1999). https://doi.org/10.1023/A:1018894417888

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