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An entropy production based method for determining the position diffusion’s coefficient of a quantum Brownian motion

  • J. Z. BernádEmail author
  • G. Homa
  • M. A. Csirik
Regular Article

Abstract

Quantum Brownian motion of a harmonic oscillator in the Markovian approximation is described by the respective Caldeira–Leggett master equation. This master equation can be brought into Lindblad form by adding a position diffusion term to it. The coefficient of this term is either customarily taken to be the lower bound dictated by the Dekker inequality or determined by more detailed derivations on the linearly damped quantum harmonic oscillator. In this paper, we explore the theoretical possibilities of determining the position diffusion term’s coefficient by analyzing the entropy production of the master equation.

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Keywords

Quantum Information 

References

  1. 1.
    A.O. Caldeira, A.J. Leggett, Physica 121A, 587 (1983) ADSCrossRefGoogle Scholar
  2. 2.
    U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999) Google Scholar
  3. 3.
    H. Grabert, P. Schramm, G.-L. Ingold, Phys. Rep. 168, 115 (1988) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    W.G. Unruh, W.H. Zurek, Phys. Rev. D 40, 1071 (1989) ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    C.H. Fleming, A. Roura, B.L. Hu, Ann. Phys. 326, 1207 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976) Google Scholar
  8. 8.
    G. Lindblad, Commun. Math. Phys. 48, 119 (1976) ADSCrossRefGoogle Scholar
  9. 9.
    R.P. Feynman, F.L. Vernon, Ann. Phys. (USA) 24, 118 (1963) ADSCrossRefGoogle Scholar
  10. 10.
    L. Diósi, Europhys. Lett. 22, 1 (1993) ADSCrossRefGoogle Scholar
  11. 11.
    J.J. Halliwell, A. Zoupas, Phys. Rev. D 52, 7294 (1995) ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    J.J. Halliwell, A. Zoupas, Phys. Rev. D 55, 4697 (1995) ADSCrossRefGoogle Scholar
  13. 13.
    I.R. Senitzky, Phys. Rev. 119, 670 (1960) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    H. Dekker, Phys. Rev. A 16, 2126 (1977) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    H. Dekker, M.C. Valsakumar, Phys. Lett. 104A, 67 (1984) ADSCrossRefGoogle Scholar
  16. 16.
    L. Diósi, Physica A 199, 517 (1993) ADSCrossRefGoogle Scholar
  17. 17.
    H. Dekker, Physica 95A, 311 (1979) ADSCrossRefGoogle Scholar
  18. 18.
    H. Spohn, J. Math. Phys. 19, 1227 (1978) Google Scholar
  19. 19.
    I. Prigogine, Science 201, 777 (1978) ADSCrossRefGoogle Scholar
  20. 20.
    L.M. Martyushev, V.D. Seleznev, Phys. Rep. 426, 1 (2006) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    P. Marian, T.A. Marian, H. Scutaru, Phys. Rev. A 69, 022104 (2004) ADSCrossRefGoogle Scholar
  22. 22.
    M. Ohya, D. Petz, Quantum Entropy and Its Use (Springer-Verlag, New York, 1993) Google Scholar
  23. 23.
    H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002) Google Scholar
  24. 24.
    A. Sandulescu, H. Scutaru, Ann. Phys. (N.Y.) 173, 277 (1987) ADSCrossRefGoogle Scholar
  25. 25.
    G. Lindblad, Commun. Math. Phys. 40, 147 (1975) ADSCrossRefGoogle Scholar
  26. 26.
    A. Uhlmann, Commun. Math. Phys. 54, 21 (1977) ADSCrossRefGoogle Scholar
  27. 27.
    K. Sato, Lévy Processes and Infinitely Divisible Distributions (Cambridge University Press, Cambridge, 1999) Google Scholar
  28. 28.
    S.M. Barnett, J.D. Cresser, Phys. Rev. A72, 022107 (2005) ADSCrossRefGoogle Scholar
  29. 29.
    A. Isar, A. Sandulescu, H. Scutaru, E. Stefanescu, W. Scheid, Int. J. Mod. Phys. E 3, 635 (1994) ADSCrossRefGoogle Scholar
  30. 30.
    M. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014) ADSCrossRefGoogle Scholar
  31. 31.
    B. Jäck, J. Senkpiel, M. Etzkorn, J. Ankerhold, C.R. Ast, K. Kern, Phys. Rev. Lett. 119, 147702 (2017) ADSCrossRefGoogle Scholar
  32. 32.
    W. Marshall, C. Simon, R. Penrose, D. Bouwmeester, Phys. Rev. Lett. 91, 130401 (2003) ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    J.Z. Bernád, L. Diósi, T. Geszti, Phys. Rev. Lett. 97, 250404 (2006) ADSCrossRefGoogle Scholar
  34. 34.
    E. Joos, H.D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, I.-O. Stamatescu, in Decoherence and the Appearance of a Classical World in Quantum Theory (Springer-Verlag, Berlin, 1996), Appendix A2 Google Scholar
  35. 35.
    S. Roman, The Umbral Calculus (Academic Press, New York, 1984) Google Scholar
  36. 36.
    E. Joos, H.D. Zeh, Z. Phys. B 59, 223 (1985) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of MaltaMsidaMalta
  2. 2.Institut für Angewandte PhysikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Department of Physics of Complex SystemsEötvös Loránd University, ELTEBudapestHungary
  4. 4.Institute for Solid State Physics and Optics, Wigner Research Centre, Hungarian Academy of SciencesBudapestHungary

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