Skip to main content
SpringerLink
Log in

Non-Markov Processes in Quantum Theory

  • Chapter
  • First Online:
Do Wave Functions Jump?

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 198))

  • 904 Accesses

Abstract

The study of quantum dynamics featuring memory effects has always been a topic of interest within the theory of open quantum system. The latter is concerned with providing useful conceptual and theoretical tools for the description of the reduced dynamics of a system interacting with an external environment. Definitions of non-Markovian processes have been introduced trying to capture the notion of memory effect by studying features of the quantum dynamical map providing the evolution of the system states, or changes in the distinguishability of the system states themselves. We introduce basic notions in the framework of open quantum systems. We stress in particular analogies and differences with models used for introducing modifications of quantum mechanics which should help in dealing with the measurement problem. We further discuss recent developments in the treatment of non-Markovian processes and their role in considering more general modifications of quantum mechanics.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. R. F. Streater, J. Math. Phys. 41, 3556 (2000)

    Google Scholar 

  2. F. Strocchi, An introduction to the mathematical structure of quantum mechanics (World Scientific, 2005)

    Google Scholar 

  3. B. Vacchini, Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics, in Theoretical Foundations of Quantum Information Processing and Communication, edited by E. Bruening and F. Petruccione (Springer, Berlin, 2010), Lecture Notes in Physics 787, pp. 39–77

    Google Scholar 

  4. M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2004)

    Google Scholar 

  5. A. Bassi and G. Ghirardi, Phys. Rep. 379, 257 (2003)

    Google Scholar 

  6. A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013)

    Google Scholar 

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

    Google Scholar 

  8. K. Hornberger, Introduction to Decoherence Theory, in Entanglement and Decoherence, edited by Andreas Buchleitner and Carlos Viviescas and Markus Tiersch (Springer, Berlin, 2009), Lecture Notes in Physics 768, pp. 221–276

    Google Scholar 

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

    Google Scholar 

  10. A. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction (Springer, 2012)

    Google Scholar 

  11. E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd edn. (Springer, Berlin, 2003)

    Google Scholar 

  12. K. M. R. Audenaert and S. Scheel, New Journal of Physics 10, 023011 (2008)

    Google Scholar 

  13. A. Pernice, J. Helm, and W. T. Strunz, Journal of Physics B: Atomic, Molecular and Optical Physics 45, 154005 (2012)

    Google Scholar 

  14. B. Vacchini, J. Phys. B 45, 154007 (2012)

    Google Scholar 

  15. D. Chruściński and F. A. Wudarski, Phys. Lett. A 377, 1425 (2013)

    Google Scholar 

  16. S. Cialdi, M. A. C. Rossi, C. Benedetti, B. Vacchini, D. Tamascelli, S. Olivares, and M. G. A. Paris, Applied Physics Letters 110, 081107 (2017)

    Google Scholar 

  17. M. A. C. Rossi, C. Benedetti, D. Tamascelli, S. Cialdi, S. Olivares, B. Vacchini, and M. G. A. Paris, International Journal of Quantum Information 15(08), 1740009 (2017)

    Google Scholar 

  18. E. B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976)

    Google Scholar 

  19. G. Ludwig, Foundations of quantum mechanics. (Springer-Verlag, New York, 1983)

    Google Scholar 

  20. K. Kraus, States, Effects, and Operations, Vol. 190 of Lecture Notes in Physics (Springer, Berlin, 1983)

    Google Scholar 

  21. A. Barchielli, L. Lanz, and G. M. Prosperi, Nuovo Cimento B 72, 79 (1982)

    Google Scholar 

  22. A. Barchielli, L. Lanz, and G. M. Prosperi, Found. Phys. 13, 779 (1983)

    Google Scholar 

  23. B. Vacchini, J. Phys. A: Math. Theor. 40, 2463 (2007)

    Google Scholar 

  24. A. Smirne, B. Vacchini, and A. Bassi, Phys. Rev. A 90, 062135 (2014)

    Google Scholar 

  25. A. S. Holevo, Rep. Math. Phys. 32, 211 (1993)

    Google Scholar 

  26. B. Vacchini, J. Math. Phys. 42, 4291 (2001)

    Google Scholar 

  27. B. Vacchini, Phys. Rev. Lett. 95, 230402 (2005)

    Google Scholar 

  28. A. Bassi, E. Ippoliti, and B. Vacchini, J. Phys. A: Math. Gen. 38, 8017 (2005)

    Google Scholar 

  29. A. Bassi and L. Ferialdi, Phys. Rev. Lett. 103, 050403 (2009)

    Google Scholar 

  30. A. Bassi and L. Ferialdi, Phys. Rev. A 80, 012116 (2009)

    Google Scholar 

  31. L. Ferialdi and A. Bassi, Phys. Rev. A 86, 022108 (2012)

    Google Scholar 

  32. L. Ferialdi and A. Bassi, Phys. Rev. Lett. 108, 170404 (2012)

    Google Scholar 

  33. L. Ferialdi and A. Smirne, Phys. Rev. A 96, 012109 (2017)

    Google Scholar 

  34. B. Vacchini, A. Smirne, E.-M. Laine, J. Piilo, and H.-P. Breuer, New J. Phys. 13, 093004 (2011)

    Google Scholar 

  35. H.-P. Breuer, J. Phys. B 45, 154001 (2012)

    Google Scholar 

  36. A. Rivas, S. F. Huelga, and M. B. Plenio, Rep. Prog. Phys. 77, 094001 (2014)

    Google Scholar 

  37. H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Rev. Mod. Phys. 88, 021002 (2016)

    Google Scholar 

  38. I. de Vega and D. Alonso, Rev. Mod. Phys. 89, 015001 (2017)

    Google Scholar 

  39. C. A. Fuchs and J. van de Graaf, IEEE Trans. Inf. Th. 45, 1216 (1999)

    Google Scholar 

  40. H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)

    Google Scholar 

  41. E.-M. Laine, J. Piilo, and H.-P. Breuer, EPL 92, 60010 (2010)

    Google Scholar 

  42. H.-P. Breuer, G. Amato, and B. Vacchini, New Journal of Physics 20, 043007 (2018)

    Google Scholar 

  43. S. Campbell, M. Popovic, D. Tamascelli, and B. Vacchini, New Journal of Physics 21, 053036 (2019)

    Google Scholar 

  44. A. Rivas, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 105, 050403 (2010)

    Google Scholar 

  45. D. Chruscinski, A. Kossakowski, and A. Rivas, Phys. Rev. A 83, 052128 (2011)

    Google Scholar 

  46. S. Wißmann, H.-P. Breuer, and B. Vacchini, Phys. Rev. A 92, 042108 (2015)

    Google Scholar 

  47. B. Vacchini, Phys. Rev. A 78, 022112 (2008)

    Google Scholar 

  48. A. Smirne and B. Vacchini, Phys. Rev. A 82, 042111 (2010)

    Google Scholar 

  49. S. L. Adler and A. Bassi, J. Phys. A: Math. Theor. 40, 15083 (2007)

    Google Scholar 

Download references

Acknowledgements

The author acknowledges support from the Joint Project “Quantum Information Processing in Non-Markovian Quantum Complex Systems” funded by FRIAS, University of Freiburg and IAR, Nagoya University, from the FFABR project of MIUR and from the Unimi Transition Grant H2020.

Author information

Authors and Affiliations

  1. Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133, Milan, Italy

    Bassano Vacchini

  2. INFN Sezione di Milano, Via Celoria 16, 20133, Milan, Italy

    Bassano Vacchini

Authors
  1. Bassano Vacchini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bassano Vacchini .

Editor information

Editors and Affiliations

  1. Department of Philosophy, Northern Illinois University, Naperville, IL, USA

    Valia Allori

  2. Department of Physics, University of Trieste, Trieste, Italy

    Angelo Bassi

  3. Mathematisches Institut, LMU, Munich, Germany

    Detlef Dürr

  4. Dipartimento di Fisica INFN-Sezion, Universitá di Genova, Genoa, Italy

    Nino Zanghi

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vacchini, B. (2021). Non-Markov Processes in Quantum Theory. In: Allori, V., Bassi, A., Dürr, D., Zanghi, N. (eds) Do Wave Functions Jump? . Fundamental Theories of Physics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-030-46777-7_24

Download citation

Publish with us

Policies and ethics

Search

Navigation