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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References
A.O. Caldeira, A.J. Leggett, Physica 121A, 587 (1983)
U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999)
H. Grabert, P. Schramm, G.-L. Ingold, Phys. Rep. 168, 115 (1988)
W.G. Unruh, W.H. Zurek, Phys. Rev. D 40, 1071 (1989)
B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)
C.H. Fleming, A. Roura, B.L. Hu, Ann. Phys. 326, 1207 (2011)
V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976)
G. Lindblad, Commun. Math. Phys. 48, 119 (1976)
R.P. Feynman, F.L. Vernon, Ann. Phys. (USA) 24, 118 (1963)
L. Diósi, Europhys. Lett. 22, 1 (1993)
J.J. Halliwell, A. Zoupas, Phys. Rev. D 52, 7294 (1995)
J.J. Halliwell, A. Zoupas, Phys. Rev. D 55, 4697 (1995)
I.R. Senitzky, Phys. Rev. 119, 670 (1960)
H. Dekker, Phys. Rev. A 16, 2126 (1977)
H. Dekker, M.C. Valsakumar, Phys. Lett. 104A, 67 (1984)
L. Diósi, Physica A 199, 517 (1993)
H. Dekker, Physica 95A, 311 (1979)
H. Spohn, J. Math. Phys. 19, 1227 (1978)
I. Prigogine, Science 201, 777 (1978)
L.M. Martyushev, V.D. Seleznev, Phys. Rep. 426, 1 (2006)
P. Marian, T.A. Marian, H. Scutaru, Phys. Rev. A 69, 022104 (2004)
M. Ohya, D. Petz, Quantum Entropy and Its Use (Springer-Verlag, New York, 1993)
H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)
A. Sandulescu, H. Scutaru, Ann. Phys. (N.Y.) 173, 277 (1987)
G. Lindblad, Commun. Math. Phys. 40, 147 (1975)
A. Uhlmann, Commun. Math. Phys. 54, 21 (1977)
K. Sato, Lévy Processes and Infinitely Divisible Distributions (Cambridge University Press, Cambridge, 1999)
S.M. Barnett, J.D. Cresser, Phys. Rev. A72, 022107 (2005)
A. Isar, A. Sandulescu, H. Scutaru, E. Stefanescu, W. Scheid, Int. J. Mod. Phys. E 3, 635 (1994)
M. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014)
B. Jäck, J. Senkpiel, M. Etzkorn, J. Ankerhold, C.R. Ast, K. Kern, Phys. Rev. Lett. 119, 147702 (2017)
W. Marshall, C. Simon, R. Penrose, D. Bouwmeester, Phys. Rev. Lett. 91, 130401 (2003)
J.Z. Bernád, L. Diósi, T. Geszti, Phys. Rev. Lett. 97, 250404 (2006)
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
S. Roman, The Umbral Calculus (Academic Press, New York, 1984)
E. Joos, H.D. Zeh, Z. Phys. B 59, 223 (1985)
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Bernád, J.Z., Homa, G. & Csirik, M.A. An entropy production based method for determining the position diffusion’s coefficient of a quantum Brownian motion. Eur. Phys. J. D 72, 212 (2018). https://doi.org/10.1140/epjd/e2018-90476-0
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DOI: https://doi.org/10.1140/epjd/e2018-90476-0