Skip to main content
SpringerLink
Log in

Description of non-Markovian effect in open quantum system with the discretized environment method

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

An approach, called discretized environment method, is used to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of discretized states with an appropriate coupling to the system of interest. The finite set of system plus environment degrees of freedom are then explicitly followed in time leading to a quasi-exact description. The present approach is anticipated to be particularly accurate in the low temperature and strongly non-Markovian regime. The discretized environment method is validated on a two-level system (qubit) coupled to a bosonic or fermionic heat-bath. A perfect agreement with the quantum Langevin approach is found. Further illustrations are made on a three-level system (qutrit) coupled to a bosonic heat-bath. Emerging processes due to strong memory effects are discussed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999)

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

  3. S. Nakajima, Prog. Theor. Phys. 20, 948 (1958)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  5. F. Hashitsume, N. Shibata, M. Shingu, J. Stat. Phys. 17, 155 (1977)

    Article  ADS  Google Scholar 

  6. F. Shibata, Y. Takahashi, N. Hashitsume, J. Stat. Phys. 17, 171 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  7. H.-P. Breuer, B. Kappler, F. Petruccione, Phys. Rev. A 59, 1633 (1999)

    Article  ADS  Google Scholar 

  8. H.-P. Breuer, B. Kappler, F. Petruccione, Ann. Phys. 291, 36 (2001)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. W.T. Strunz, Phys. Lett. A 224, 25 (1996)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. L. Diosi, N. Gisin, W.T. Strunz, Phys. Rev. A 58, 1699 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  11. W.T. Strunz, L. Diosi, N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. W.T. Strunz, New J. Phys. 7, 91 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  13. J. Piilo, S. Maniscalco, K. Härkönen, K.-A. Suominen, Phys. Rev. Lett. 100, 180402 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  14. Z. Kanokov, Yu.V. Palchikov, G.G. Adamian, N.V. Antonenko, W. Scheid, Phys. Rev. E 71, 016121 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  15. Yu.V. Palchikov, Z. Kanokov, G.G. Adamian, N.V. Antonenko, W. Scheid, Phys. Rev. E 71, 016122 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  16. G.G. Adamian, N.V. Antonenko, Z. Kanokov, V.V. Sargsyan, Theor. Math. Phys. 145, 1443 (2005)

    Article  MATH  Google Scholar 

  17. V.V. Sargsyan, Z. Kanokov, G.G. Adamian, N.V. Antonenko, Phys. Rev. C 77, 024607 (2008)

    Article  ADS  Google Scholar 

  18. V.V. Sargsyan, Z. Kanokov, G.G. Adamian, N.V. Antonenko, Phys. Part. Nuclei 41, 175 (2010)

    Article  ADS  Google Scholar 

  19. R.A. Kuzyakin, V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 83, 062117 (2011)

    Article  ADS  Google Scholar 

  20. R.A. Kuzyakin, V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, Phys. Rev. A 84, 032117 (2011)

    Article  ADS  Google Scholar 

  21. K. Wen, F. Sakata, Z.-X. Li, X.-Z. Wu, Y.-X. Zhang, S.-G. Zhou, Phys. Rev. Lett. 111, 012501 (2013)

    Article  ADS  Google Scholar 

  22. J. Shao, J. Chem. Phys. 120, 5053 (2004)

    Article  ADS  Google Scholar 

  23. D. Lacroix, Phys. Rev. A 72, 013805 (2005)

    Article  ADS  Google Scholar 

  24. D. Lacroix, Phys. Rev. E 77, 041126 (2008)

    Article  ADS  Google Scholar 

  25. G. Hupin, D. Lacroix, Phys. Rev. C 81, 014609 (2010)

    Article  ADS  Google Scholar 

  26. H.-P. Breuer, Eur. Phys. J. D 29, 105 (2004)

    Article  ADS  Google Scholar 

  27. P. Rebentrost, R. Chakraborty, A. Aspuru-Guzik, J. Chem. Phys. 131, 184102 (2009)

    Article  ADS  Google Scholar 

  28. Q. Ai, Y.-J. Fan, B.-Y. Jin, Y.-C. Cheng, New J. Phys. 16, 053033 (2014)

    Article  ADS  Google Scholar 

  29. J. Jing, T. Yu, Phys. Rev. Lett. 105, 240403 (2010)

    Article  ADS  Google Scholar 

  30. M. Topaler, N. Makri, J. Chem. Phys. 101, 7500 (1994)

    Article  ADS  Google Scholar 

  31. J.P. Paz, A.J. Roncaglia, Phys. Rev. A 80, 042111 (2009)

    Article  ADS  Google Scholar 

  32. C. Lazarou, K. Luoma, S. Maniscalco, J. Piilo, B.M. Garraway, Phys. Rev. A 86, 012331 (2012)

    Article  ADS  Google Scholar 

  33. R. Vasile, F. Galve, R. Zambrini, Phys. Rev. A 89, 022109 (2014)

    Article  ADS  Google Scholar 

  34. V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, D. Lacroix, Phys. Rev. A 90, 022123 (2014)

    Article  ADS  Google Scholar 

  35. B.J. Dalton, B.M. Garraway, Phys. Rev. A 68, 033809 (2003)

    Article  ADS  Google Scholar 

  36. K. Lindenberg, B.J. West, The Nonequilibrium Statistical Mechanics of Open and Closed Systems (VCH Publishers Inc., New York, 1990)

  37. E.G. Harris, Phys. Rev. C 48, 995 (1993)

    Article  ADS  Google Scholar 

  38. P.W. Milonni, J.R. Ackerhalt, H.W. Galbraith, M.-L. Shih, Phys. Rev. A 28, 32 (1983)

    Article  ADS  Google Scholar 

  39. H.M. Lai, P.T. Leung, K. Young, Phys. Rev. A 37, 1597 (1988)

    Article  ADS  Google Scholar 

  40. B.M. Garraway, Phys. Rev. A 55, 4636 (1997)

    Article  ADS  Google Scholar 

  41. B.M. Garraway, Phys. Rev. A 55, 2290 (1997)

    Article  ADS  Google Scholar 

  42. R.H. Dicke, Phys. Rev. 93, 99 (1954)

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, 91406, Orsay Cedex, France

    Denis Lacroix

  2. Yerevan State University, M. Manougian 1, 0025, Yerevan, Armenia

    Vazgen Sargsyan

  3. Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vazgen Sargsyan, Gurgen Adamian & Nikolai Antonenko

Authors
  1. Denis Lacroix
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vazgen Sargsyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gurgen Adamian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nikolai Antonenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lacroix, D., Sargsyan, V., Adamian, G. et al. Description of non-Markovian effect in open quantum system with the discretized environment method. Eur. Phys. J. B 88, 89 (2015). https://doi.org/10.1140/epjb/e2015-60052-3

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2015-60052-3

Keywords

Search

Navigation