Abstract
The environment surrounding a quantum system can, in effect, monitor some of the systems observables. As a result, the eigenstates of these observables continuously decohere and can behave like classical states.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Further Reading
A. Albrecht, Investigating Decoherence in a Simple System, Phys. Rev. D 46(12), 5504 (1992).
J. R. Anglin and W. H. Zurek, Decoherence of Quantum Fields: Pointer States and Predictability, Phys. Rev. D 53(12), 7327 (1996).
J. R. Anglin, J. P. Paz and W. H. Zurek, Deconstructing Decoherence, Phys. Rev. A 55(6), 4041 (1997).
M. Arndt, O. Nairz, J. VosAndreae, C. Keller, G. van der Zouw, A. Zeilinger, Wave-Particle Duality of C-60 Molecules, Nature 401(6754), 680 (1999).
A. Aspect, J. Dalibard and G. Roger, Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers, Phys. Rev. Lett. 49, 1804 (1982).
A. Aspect, P. Grangier and G. Rogier, Experimental Tests of Realistic Local Theories via Bell’s Theorem, Phys. Rev. Lett. 47, 460 (1981).
J. S. Bell, On the Einstein Podolsky Rosen Paradox, Physics 1, 195 (1964).
D. Bohm, In Quantum Theory, Chap. 22, p. 611. Englewood Cliffs, NJ: Prentice Hall, 1951.
N. Bohr, The Quantum Postulate and Recent Development of Atomic Theory, Nature 121, 580 (1928). Reprinted in Quantum Theory and Measurement. Edited by Wheeler, J. A., and W. H. Zurek. Princeton, NJ: Princeton University Press.
V.B. Braginsky, Y. I. Vorontsov and K. S. Thorne, Quantum Nondemolition Measurements, Science 209, 547 (1980).
M. Brune, E. Hagley, J. Dreyer, X. Maitre, C. Wunderlich, J. M. Raimond and S. Haroche, Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement, Phys. Rev. Lett. 77, 4887 (1996).
A. O. Caldeira, and A. J. Leggett, Path Integral Approach to Quantum Brownian Motion, Physica A 121, 587 (1983a).
—, Quantum Tunneling in a Dissipative System, Ann. Phys (N. Y.) 149(2), 374 (1983b).
—, Influence of Damping on Quantum Interference: An Exactly Soluble Model, Phys. Rev. A 31, 1059 (1985).
H. J. Carmichael, An Open Systems Approach to Quantum Optics, Berlin, Springer Verlag, 1993.
C. M. Caves, K. S. Thorne, R. W. P. Drewer, V. D. Sandberg and M. Zimmerman, On the Measurement of a Weak Classical Force Coupled to a Quantum-Mechanical Oscillator, 1. Issues of Principle. Rev. Mod. Phys. 52, 341 (1980).
M. S. Chapman, T. D. Hammond, A. Lenef, J. Schmiedmayer, R. A. Rubenstein, E. Smith and D. E. Pritchard, Photon Scattering from Atoms in an Atom Interferometer, Phys. Rev. Lett. 75(21), 3783 (1995).
C. C. Cheng and M. G. Raymer, Long-Range Saturation of Spatial Decoherence in Wave-Field Transport in Random Multiple-Scattering Media, Phys. Rev. Lett. 82 (24), 4807 (1999).
D. A. R. Dalvit, J. Dziarmaga, W. H. Zurek, Unconditional Pointer States from Conditional Master Equations, Phys. Rev. Lett. 86(3), 373 (2001).
H. Dekker, Classical and Quantum Mechanics of the Damped Harmonic Oscillator, Phys. Rep. 80, 1 (1981).
B. S. DeWitt, Quantum Mechanics and Reality, Phys. Today 23, 30 (1970).
B. S. DeWitt and N. Graham, eds., The Many-Worlds Interpretation of Quantum Mechanics. Princeton: Princeton University Press, 1973.
A. Einstein, B. Podolsky and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 777 (1935).
H. Everett III, “Relative State” Formulation of Quantum Mechanics, Rev. Mod. Phys. 29, 454 (1957).
R. P. Feynman and F. L.Vernon, The Theory of a General Quantum System Interacting with a Linear Dissipative System, Ann. Phys. 24, 118 (1963).
J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo and J. E. Lukens, Quantum Superposition of Distinct Macroscopic States, Nature 406(6791), 43 (2000).
C. A. Fuchs and A. Peres, Quantum Theory Needs No “Interpretation”, Phys. Today 53(3), 70 (2000).
M. R. Gallis, Emergence of Classicality via Decoherence Described by Lindblad Operators, Phys. Rev. A 53(2), 655 (1996).
M. Gell-Mann and J. B. Hartle, Quantum Mechanics in the Light of Quantum Cosmology, In Complexity, Entropy, and the Physics of Information. p. 425. Edited by W. H. Zurek. Redwood City: Addison-Wesley, 1990.
R. B. Griffiths, Consistent Histories and the Interpretation of Quantum Mechanics, J. Stat. Phys. 36, 219 (1984).
F. Haake and D. F. Walls, In Quantum Optics IV. Edited by J. D. Harvey, and D. F. Walls. Berlin: Springer Verlag, 1986.
S. Habib, K. Shizume and W. H. Zurek, Decoherence, Chaos, and the Correspondence Principle, Phys. Rev. Lett. 80(20), 4361 (1998).
S. Haroche, Entanglement, Mesoscopic Superpositions and Decoherence Studies with Atoms and Photons in a Cavity, Physica Scripta T76, 159 (1998).
J. B. Hartle, The Quantum Mechanics of Cosmology. In Quantum Cosmology and Baby Universes, Proceedings of the 1989 Jerusalem Winter School. Edited by S. Coleman, J. B. Hartle, T. Piran, and S. Weinberg. Singapore: World Scientific, 1991.
B. L. Hu, J. P. Paz and Y. Zhang, Quantum Brownian Motion in a General Environment: Exact Master Equation with Nonlocal Dissipation and Colored Noise, Phys. Rev. D 45, 2843 (1992).
E. Joos and H. D. Zeh, The Emergence of Classical Properties Through Interaction with the Environment. Z., Phys. B 59 223 (1985).
Z. P. Karkuszewski, J. Zakrzewski and W. H. Zurek, Breakdown of Correspondence in Chaotic Systems: Ehrenfest Versus Localization Times, Phys. Rev. A 65(4), 042113 (2002).
D. A. Kokorowski, A. D. Cronin, T. D. Roberts and D. E. Pritchard, From Single-to Multiple-Photon Decoherence in an Atom Interferometer, Phys. Rev. Lett. 86(11), 2191 (2001).
R. Landauer, Information is Physical, Phys. Today 44(5), 23 (1991).
A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger, Dynamics of the Dissipative System, Rev. Mod. Phys. 59, 1 (1987).
G. J. Milburn and C. A. Holmes, Dissipative Quantum and Classical Liouville Mechanics of the Unharmonic Oscillator, Phys. Rev. Lett. 56, 2237 (1986).
P. A. Miller and S. Sarkar, Signatures of Chaos in the Entanglement of Two Coupled Quantum Kicked Tops, Phys. Rev. E 60, 1542 (1999).
C. Monroe, D. M. Meekhof, B. E. King and D. J. Wineland, A “Schrödinger Cat” Superposition State of an Atom, Science 272(5265), 1131 (1996).
D. Monteoliva and J. P. Paz, Decoherence and the Rate of Entropy Production in Chaotic Quantum Systems, Phys. Rev. Lett. 85(16), 3373 (2000).
J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal and S. Lloyd, Josephson Persistent-Current Qubit, Science 285(5430), 1036 (1999).
C. J.Myatt, B. E. King, Q. A. Turchette, C. A. Sackett, D. Kielpinski, W. M. Itano, et al, Decoherence of Quantum Superpositions Through Coupling to Engineered Reservoirs, Nature 403, 269 (2000).
H. Ollivier and W. H. Zurek, Quantum Discord: A Measure of the Quantumness of Correlations, Phys. Rev. Lett. 88(1), 017901 (2002).
R. Omnés, From Hilbert Space to Common Sense, Ann. Phys. 201, 354 (1990).
—, Consistent Interpretation of Quantum Mechanics, Rev. Mod. Phys 64, 339 (1992).
A. K. Pattanayak, Lyapunov Exponents Entropy Production and Decoherence, Phys. Rev. Lett. 83(22), 4526 (1999).
J. P. Paz and W. H. Zurek, Environment-Induced Decoherence, Classicality, and Consistency of Quantum Histories, Phys. Rev. D 48(6), 2728 (1993).
—, Quantum Limit of Decoherence: Environment Induced Superselection of Energy Eigenstates, Phys. Rev. Lett. 82(26), 5181 (1999).
—, In Coherent Atomic Matter Waves, Les Houches Lectures, Edited by R. Kaiser, C. Westbrook, and F. Davids. Vol. 72, p. 533. Berlin: Springer, 2001.
J. P. Paz, S. Habib and W. H. Zurek, Reduction of the Wave Packet: Preferred Observable and Decoherence Time Scale, Phys. Rev. D 47, 488 (1993).
T. Pfau, S. Splater, Ch. Kurtsiefer, C. R. Ekstrom and J. Mlynek, Loss of Spatial Coherence by a Single Spontaneous Emission, Phys. Rev. Lett. 73(9), 1223 (1994).
M. O. Scully, B. G. Englert and J. Schwinger, Spin Coherence and Humpty-Dumpty. III. The Effects of Observation, Phys. Rev. A 40, 1775 (1989).
M. C. Teich and B. E. A. Saleh, Squeezed and Antibunched Light, Phys. Today 43(6), 26 (1990).
C. D. Tesche, Schrödinger’s Cat: A Realization in Superconducting Devices, Ann. N. Y. Acad. Sci. 480, 36 (1986).
Q. A. Turchette, C. J. Myatt, B. E. King, C. A. Sackett, D. Kielpinski, W. M. Itano, et al, Decoherence and Decay of Motional Quantum States of a Trapped Atom Coupled to Engineered Reservoirs, Phys. Rev. A 62, 053807 (2000).
W. G. Unruh and W. H. Zurek, Reduction of a Wave Packet in Quantum Brownian Motion, Phys. Rev. D. 40, 1071 (1989).
J. Von Neumann, Mathematische Grundlagen der Quanten Mechanik. Berlin: Springer-Verlag, English translation by R. T. Beyer. 1955. Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press, 1932.
J. A. Wheeler, Assessment of Everett’s “Relative State” Formulation of Quantum Theory, Rev. Mod. Phys. 29, 463 (1957).
—, Information, Physics, Quantum: The Search for Links, In Complexity, Entropy, and the Physics of Information. p. 3. Edited by W. H. Zurek. Redwood City: Addison-Wesley, 1991.
J. A. Wheeler and W. H. Zurek, eds., Quantum Theory and Measurement, Princeton: Princeton University Press, 1983.
E. P. Wigner, On the Quantum Correction for Thermodynamic Equilibrium, Phys. Rev. 40, 749 (1932).
—, Remarks on the Mind-Body Question, In The Scientist Speculates, p. 284. Edited by I. J. Good. London: Heineman, 1961.
—, The Problem of Measurement, Am. J. Phys. 3, 615 (1963).
—, In Quantum Optics, Experimental Gravitation, and the Measurement Theory, Edited by P. Meystre, and M. O. Scully. p. 43. New York: Plenum Press, 1983.
H. D. Zeh, On the Interpretation of Measurement in Quantum Theory, Found. Phys. 1, 69 (1970).
W. H. Zurek, Pointer Basis of Quantum Apparatus: Into What Mixture Does the Wave Packet Collapse?, Phys. Rev. D 24, 1516 (1981).
—, Environment-Induced Superselection Rules, Phys. Rev. D 26, 1862 (1982).
—, Reduction of the Wave Packet: How Long Does It Take? In Frontiers of Nonequilibrium Statistical Physics, Edited by P. Meystre, and M. O. Scully. New York: Plenum, 1984.
—, Decoherence and the Transition From Quantum to Classical, Phys. Today 44(10), 36 (1991).
—, Preferred States, Predictability, Classicality, and the Environment-Induced Decoherence, Prog. Theor. Phys. 89(2), 281 (1993).
—, Decoherence, Chaos, Quantum-Classical Correspondence, and the Algorithmic Arrow of Time, Physica Scripta T76, 186 (1998).
—, Einselection and Decoherence from an Information Theory Perspective, Ann. Phys. (Leipzig) 9(11–12), 855 (2000).
—, Decoherence, Einselection, and the Quantum Origins of the Classical, (2001a), http://eprints.lanl.gov. quant-ph/0105127.
—, Sub-Planck Structure in Phase Space and its Relevance for Quantum Decoherence, Nature 412, 712 (2001b).
W. H. Zurek and J. P. Paz, Decoherence, Chaos, and the Second Law, Phys. Rev. Lett. 72(16), 2508 (1994).
—, Quantum Chaos: A Decoherent Definition, Physica D 83(1–3), 300 (1995).
W. H. Zurek, S. Habib and J. P. Paz, Coherent States via Decoherence, Phys. Rev. Lett. 70(9), 1187 (1993).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Zurek, W.H. (2006). Decoherence and the Transition from Quantum to Classical — Revisited. In: Duplantier, B., Raimond, JM., Rivasseau, V. (eds) Quantum Decoherence. Progress in Mathematical Physics, vol 48. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7808-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7808-0_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7807-3
Online ISBN: 978-3-7643-7808-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)