Abstract
We study dynamics of quantum open systems, paying special attention to these aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced supers election (einselection) in a more general setting, we sketch perturbative as well as exact derivations of several master equations valid for various systems. Using these equations we study einselection employing the general strategy of the predictability sieve. Assumptions that are usually made in the discussion of decoherence are critically reexamined along with the “standard lore” to which they lead. Restoration of quantum-classical correspondence in systems that are classically chaotic is discussed. The dynamical second law - it is shown - can be traced to the same phenomena that allow for the restoration of the correspondence principle in decohering chaotic systems (where it is otherwise lost on a very short time-scale). Quantum error correction is discussed as an example of an anti-decoherence strategy. Implications of decoherence and einselection for the interpretation of quantum theory are briefly pointed out.
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References
W.H. Zurek, Phys. Rev. D 24 (1981) 1516–1524.
W.H. Zurek, Phys. Rev. D 26 (1982) 1862–1880.
W.H. Zurek, Progr. Theor. Phys. 89 (1993) 281–302.
W.H. Zurek, S. Habib and J.P. Paz, Phys. Rev. Lett. 70 (1993) 1187–1190; J.R. Anglin and W.H. Zurek, Phys. Rev. D 53 (1996) 7327–7335.
M.R. Gallis, Phys. Rev. A 53 (1996) 655–660; M. Tegmark and H.S. Shapiro, Phys. Rev. E 50 2538–2547 (1994).
M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J.-M. Raimond and S. Haroche, Phys. Rev. Lett. 77 (1996) 4887–4890.
C.C. Cheng and M.G. Raymer, Phys. Rev. Lett. 82 (1999) 4802.
C.J. Myatt et al., Nat 403 (2000) 269.
H. Ammann, R. Gray, I. Shvarchuk and N. Christensen, Phys. Rev. Lett. 80 (1998) 4111.
B.G. Klappauf, W.H. Oskay, D.A. Steck and M.G. Raizen, Phys. Rev. Lett. 81 (1998) 1203; Erratum in Phys Rev. Lett. 82 (1999) 241.
C.H. Bennett, Phys. Today 48, No. 10 (1995); C.H. Bennett and D.P. DiVincenzo, Nat 404 (2000) 247.
W.K. Wootters and W.H. Zurek, Nat 299 (1982) 802.
D. Dieks, Phys. Lett. A 92 (1982) 271.
W.H. Zurek, Phys. Today 44 (1991) 36.
M. Tegmark, Phys. Rev. E 61 (2000) 4194.
W.H. Zurek, Phys. Scr. T 76 (1998) 186, also available at [quant-ph/9802054].
W.H. Zurek, Phil. Trans. R. Soc. Lond. A 356 (1998) 1793, also available at [quant-ph/9805065].
J. von Neumann, Measurement and reversibility and The measuring process, Chapters V and VI if Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932); English translation by R.T. Beyer, Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, 1955).
Monroe, C., Meekhof, D.M., King, B.E., and Wineland, D.J., Sci 272 (1996) 1131–1136.
Everett III, H., Rev. Mod. Phys. 29 (1957) 454.
W.H. Zurek, in Physical Origins of Time Asymmetry, edited by J.J. Halliwell, J. Pérez-Mercader and W.H. Zurek (Cambridge University Press, Cambridge, 1994) pp. 175–212.
W.H. Zurek, Information transfer in quantum measurements, in Quantum Optics, Experimental Gravity, and the Measurement Theory, edited by P. Meystre and M.O. Scully (Plenum, New York, 1983) pp. 87–116.
D. Bohm, Quantum Theory, (Prentice-Hall, Engelwood Cliffs, 1951).
H. Rauch, Phys. Scr. T76 (1998) 24.
T. Pfau et al., Phys. Rev. Lett. 73 (1994) 1223.
M.S. Chapman et al., Phys. Rev. Lett. 75 (1995) 3783.
W.H. Zurek (2000) (in preparation).
S. Lloyd, Phys. Rev. A 55 (1996) 1613.
B. Schumacher, Phys. Rev. A 54 (1996) 2614.
R. Landauer, Phil Trans. R. Soc. 353 (1995) 367; also, in Proc. of the Drexel-4 Symposium on Quantum Nonintegrability: Quantum-Classical Correspondence, edited by D.H. Feng and B.-L. Hu (World Scientific, Singapore, 1998); W.G. Unruh, Phys. Rev A. 51 (1995) 992; I.L. Chuang, R. Laflamme, P. Shor and W.H. Zurek, Sci 270 (1995) 1633–1635.
H.D. Zeh, Found. Phys. 3 (1973) 109.
H.D. Zeh, The Physical Basis of the Direction of Time (Springer, Berlin, 1989).
A. Albrecht, Phys. Rev. D 46 (1992) 5504.
A. Albrecht, Phys. Rev. D 48 (1993) 3768.
D.F. Walls and G.J. Milburn, Quant. Opt. (Springer Verlag, Berlin, 1994).
S. Chaturvedy and F. Shibata, Z. Phys. B35 (1979) 297, see also M. Desposito and S.H. Hernandez, Physica 227A (1996) 248.
B.L. Hu, J.P. Paz and Y. Zhang, Phys. Rev. D 45 (1992) 2843.
A. J. Leggett, S. Chakravarty, A.T. Dorsey, M.P.A. Fisher, A. Garg and W. Zwerger, Rev. Mod. Phys. 59 (1987) 1.
J.P. Paz, in Physical Origin of Time Asymmetry, edited by J.J. Halliwell, J. Pérez-Mercader and W.H. Zurek (Cambridge University Press, 1992) pp. 213–220.
A.O. Caldeira and A.J. Leggett, Physica 121A, (1983) 587–616; Phys. Rev. A 31 (1985) 1059.
W.G. Unruh and W.H. Zurek, Phys. Rev. D 40 (1989) 1071–1094.
F. Haake and R. Reibold, Phys. Rev. 32 (1985) 2462.
B.L. Hu, J.P. Paz, and Y. Zhang, Phys. Rev. D 47 (1993) 1576.
H. Grabert, P. Shramm and G.L. Ingold, Phys. Rep. 168 (1988) 115.
L. Dávila Romero and J.P. Paz, Phys. Rev. A 55 (1997) 4070.
R.P. Feynman and F.L. Vernon, Ann. Phys. 24 (1963) 118.
J.P. Paz, S. Habib and W.H. Zurek, Phys. Rev. D 47 (1993) 488.
E.P. Wigner, Phys. Rev. 40 (1932) 749. For a review, see M. Hillery, R.F. O’Connell, M.O. Scully and E.P. Wigner, Phys. Rep. 106 121 (1984).
G. Lindblad, Comm. Math. Phys. 40 (1976) 119–130.
B.M. Garraway, Phys. Rev. A 55 (1997) 4636; ibid A 55 (1997) 2290.
C. Anastopoulos and B.L. Hu, [e-print quant-ph/9901078].
W.H. Zurek, in Frontiers of Non-equilibrium Statistical Mechanics, edited by G.T. Moore and M.O. Scully (Plenum, New York, 1986) pp. 145–149.
W.H. Zurek, S. Habib and J.P. Paz, Phys. Rev. Lett. 70 (1993) 1187.
J.P. Paz and W.H. Zurek, Phys. Rev. Lett. 82 (1999) 5181.
J.R. Anglin, J.P. Paz and W.H. Zurek, Phys. Rev. A 53 (1997) 4041.
M.R. Gallis and G.N. Fleming, Phys. Rev. A 42 (1990) 38; A 43 (1991) 5778; M.R. Gallis, Phys. Rev. A 48 (1993) 1023.
J. Wisdom, S.J. Peale and F. Maignard, Icarus 58 (1984) 137; see also J. Wisdom, Icarus 63 (1985) 272.
J. Laskar, Nat 338 (1989) 237.
G.J. Sussman and J. Wisdom, Sci 257 (1992) 56–62.
W.H. Zurek and J.P. Paz, Phys. Rev. Lett. 72 (1994) 2508–2511; ibid 75 (1995) 351.
W.H. Zurek and J.P. Paz, Physica D83 (1995) 300.
see selected papers in Casati, G., and Chrikov, B., Quantum Chaos (Cambridge University Press, Cambridge, 1995).
G.P. Berman and G.M. Zaslavsky, Physica A 91 (1978) 450.
S. Habib, K. Shizume, and W.H. Zurek, Phys. Rev. Lett. 80 (1998) 4361.
E. Ott, T.M. Antonsen and J. Hanson, Phys. Rev. Lett. 35 (1984) 2187; T. Dittrich and R. Graham, Phys. Rev. A 42 (1990) 4647, and references therein.
This point of view is related to the one expressed by C. Caves et al. who emphasize on “hipersensitivity to perturbations” as the defining aspect of quantum chaos. See C. Caves and R. Schack, Hypersensitivity to perturbation: An information-theoretical characterization of classical and quantum chaos, in Quantum Communication, Computing, and Measurement, edited by O. Hirota, A.S. Holevo and C.M. Caves (Plenum Press, New York, 1997) pp. 317–330. This criterion was introduced by A. Peres (see A. Peres, Quantum Theory Concepts and Methods (Kluger, 1995)).
K. Shiokawa and B.L. Hu, Phys. Rev. E 52 (1995) 2497.
P.A. Miller and S. Sarkar, Phys. Rev. E 58 (1998) 4217; E 60 (1999) 1542.
A.K. Pattanayak, Phys. Rev. Lett. 83 (2000) 4526.
H. Pastawski, C Usaj and P. Levstein, “Quantum chaos: an answer to the Boltzmann-Loschmidt controversy?”, preprint Famaf (2000); for interesting related experimental work using NMR techniques see also H. Pastawski, C Usaj and P. Levstein, Chem. Phys. Lett. 261 (1996) 329.
D. Monteoliva and J.P. Paz (2000) (to appear).
M. Gell-Mann and J.B. Hartle, in Complexity, Entropy, and the Physics of Information, edited by W.H. Zurek (Addison-Wesley, Reading, 1990).
D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H.D. Zeh, Deco-herence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996).
A. Steane, Phys. Rev. Lett. 77 (1996) 793; A. Steane, Proc. Roy. Soc. Lond. A 452 (1996) 2551.
P. Shor, Phys. Rev. A 52 (1995) 2493.
McWilliams and Sloane, “Theory of Error Correcting Codes” (Elsevier, Amsterdam, 1977).
R. Laflamme, C. Miquel, J.P. Paz and W.H. Zurek, Phys. Rev. Lett. 77 (1996) 198.
J.P. Paz and W.H. Zurek, Proc. Roy. Soc. London A 454 (1998) 355.
A.R. Calderbank, E.M. Rains, P.W. Shor and N.J.A. Sloane, Phys. Rev. Lett. 78 (1997) 405.
D. Gottesman, Caltech Ph.D. Thesis, quant-ph, see also “Stabilizer codes and quantum error correction”, Preprint (1998) [quant-ph/9705052]; Phys. Rev. A 54 (1996) 1862.
E. Knill and R. Laflamme, Preprint [quant-ph/9608012]; Phys. Rev. A 55 (1997) 900.
R. Cleve and D. Gottesman, Phys. Rev. 56 (1997) 76.
H. Pringe, MsC Thesis, Buenos Aires University (1997) (unpublished).
J.J. Halliwell, Phys. Rev. D 39 (1989) 2912; C. Kiefer, Class. Quantum Grav. 4 (1987) 1369; J.P. Paz and S. Sinha, Phys. Rev. D 45 (1992) 2823; ibid D 44 (1991) 1038; for more recent discussion see F. Lombardo, F.D. Mazzitelli and D. Monteoliva, Phys. Rev. D (2000) (to appear).
J.F. Poyatos, J.I. Cirac and P. Zoller, Phys. Rev. Lett. 77 (1997) 4728.
L. Davidovich, M. Brune, J.M. Raimond and S. Haroche, Phys. Rev. A 53 (1996) 1295.
D. Dalvit and P. Maia Neto, Phys. Rev. Lett. 87 (2000) 798; see also [quant-ph/0004057].
J. Anglin, Phys. Rev. Lett. 79 (1997) 6.
D. Dalvit, J. Dziamarmaga and W.H. Zurek, Phys. Rev. A (2000) (to appear).
P. Mohanty, E.M.Q. Jariwada and R.A. Webb, Phys. Rev. Lett. 77 (1995) 3366; P. Mohanty and R.A. Webb, Phys. Rev. B 55 (1997) R13 452.
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Paz, J.P., Zurek, W.H. (2001). Environment-Induced Decoherence and the Transition from Quantum to Classical. In: Kaiser, R., Westbrook, C., David, F. (eds) Coherent atomic matter waves. Les Houches - Ecole d’Ete de Physique Theorique, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45338-5_8
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