Skip to main content
Log in

A quantum trajectory description of decoherence

  • Molecular Physics and Chemical Physics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract.

A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of degrees of freedom, this making the problem numerically intractable from a purely quantum-mechanical point of view. To overcome this drawback, a new class of quantum trajectories is proposed. These trajectories, based on the same grounds as Bohmian ones, are solely associated to the system reduced density matrix, since the evolution of the environment degrees of freedom is not considered explicitly. Within this approach, environment effects come into play through a time-dependent damping factor that appears in the system equations of motion. Apart from their evident computational advantage, this type of trajectories also results very insightful to understand the system decoherence. In particular, here we show the usefulness of these trajectories analyzing decoherence effects in interference phenomena, taking as a working model the well-known double-slit experiment.

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

  • R. Omnès, Rev. Mod. Phys. 64, 339 (1992)

    Article  ADS  Google Scholar 

  • W.H. Zurek, Physics Today 44, 36 (1991)

    Google Scholar 

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

  • C. Kiefer, E. Joos, Decoherence: Concepts and Examples, in Quantum Future, edited by P. Blanchard, A. Jadczyk (Springer, Berlin, 1998)

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

    Article  ADS  Google Scholar 

  • M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

  • W.G. Unruh, Phys. Rev. A 51, 992 (1995); R. Landauer, Phys. Lett. A 217, 188 (1996); S. Mancini, R. Bonifacio, Phys. Rev. A 63, 032310 (2001)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

  • A.S. Sanz, F. Borondo, S. Miret-Artés, Phys. Rev. B 61, 7743 (2000)

    Article  ADS  Google Scholar 

  • C. Philippidis, C. Dewdney, B.J. Hiley, Nuovo Cimento B 52, 15 (1979); C. Philippidis, D. Bohm, R.D. Kaye, Nuovo Cim. B 71, 75 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  • H.M. Wiseman, Phys. Rev. A 58, 1740 (1998)

    Article  ADS  Google Scholar 

  • P. Ghose, A.S. Majumdar, S. Guha, J. Sau, Phys. Lett. A 290, 205 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • A.S. Sanz, F. Borondo, S. Miret-Artés, J. Phys.: Condens. Matter 14, 6109 (2002)

    Article  ADS  Google Scholar 

  • R. Guantes, A.S. Sanz, J. Margalef-Roig, S. Miret-Artés Surf. Sci. Rep. 53, 199 (2004)

    Article  Google Scholar 

  • E. Guay, L. Marchildon, Preprint arXiv:quant-ph/0407077 (2004)

  • H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

  • W.K. Wootters, W.H. Zurek, Phys. Rev. D 19, 473 (1979); R. Bhandari, Phys. Rev. Lett. 69, 3720 (1992); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); H.M. Wiseman, F.E. Harrison, M.J. Collet, S.M. Tan, D.F. Walls, R.B. Killip, Phys. Rev. A 56, 55 (1997); G. Björk, A. Karlsson, Phys. Rev. A 58, 3477 (1998); S. Dürr, Phys. Rev. A 64, 042113 (2001)

    Article  ADS  Google Scholar 

  • S. Dürr, T. Nonn, G. Rempe, Phys. Rev. Lett. 81, 5705 (1998)

    Article  ADS  Google Scholar 

  • A. Zeilinger, R. Gähler, C.G. Shull, W. Treimer, W. Mampe, Rev. Mod. Phys. 60, 1067 (1988)

    Article  ADS  Google Scholar 

  • D.M. Appleby, Found. Phys. 29, 1885 (1999)

    Article  MathSciNet  Google Scholar 

  • V. Viale, M. Vicari, N. Zanghì, Phys. Rev. A 68, 063610 (2003)

    Article  ADS  Google Scholar 

  • A.S. Sanz, F. Borondo, M. Bastiaans, Phys. Rev. A 71 42103 (2005)

    Google Scholar 

  • Quantum Dynamics of Complex Molecular Systems, edited by D. Micha, I. Burghardt (Springer, Berlin, 2006)

  • (a) W.H. Miller, J. Chem. Phys. 53, 3578 (1970); (b) W.H. Miller, Faraday Discuss. 110, 1 (1998); (c) R. Gelabert, X. Giménez, M. Thoss, H. Wang, W.H. Miller, J. Phys. Chem. A 104, 10321 (2000); (d) R. Gelabert, X. Giménez, M. Thoss, H. Wang, W.H. Miller, J. Chem. Phys. 114, 2562 (2001); (e) R. Gelabert, X. Giménez, M. Thoss, H. Wang, W.H. Miller, J. Chem. Phys. 114, 2572 (2001); (f) S. Zhang, E. Pollak, J. Chem. Phys. 121, 3384 (2004)

    Article  ADS  Google Scholar 

  • R.P. Feynman, Rev. Mod. Phys. 20, 367 (1948); R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965)

    Article  ADS  MathSciNet  Google Scholar 

  • Quantum Dynamics of Open Systems, edited by P. Pechukas, U. Weiss, special issue in Chem. Phys. 268 (2001)

  • I. Percival, Quantum State Diffusion (Cambridge University Press, Cambridge, 1998)

  • R. Omnès, Phys. Rev. A 56, 3383 (1997)

    Article  ADS  Google Scholar 

  • C.M. Savage, D.F. Walls, Phys. Rev. A 32, 2316, 3487 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  • T. Qureshi, A. Venugopalan, Int. J. Mod. Phys. (to appear, 2007); Preprint arXiv:quant-ph/0602052

  • A.S. Sanz, F. Borondo, S. Miret-Artés, Europhys. Lett. 55, 303 (2002)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. Borondo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sanz, A., Borondo, F. A quantum trajectory description of decoherence. Eur. Phys. J. D 44, 319–326 (2007). https://doi.org/10.1140/epjd/e2007-00191-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2007-00191-8

PACS.

Navigation