By Duplantier B., Raimond J.-M., Rivasseau V.
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Extra resources for Quantum Decoherence. Poincare Seminar
Example text
38) and (39), noting finally that P|x /2 = | − x /2 [see Eq. (32)], we get: 2 T r[D(−α)ρD(α)P] . (40) π The Wigner distribution at α is the expectation value in the state translated by −α of the field parity operator. 2. 5. 1. Master equation. Decoherence is the result of a dissemination of information about a system via its entanglement with an environment E. For all practical purposes, this information is buried in E on which no measurement can be performed in practice. The system density operator ρ is obtained by tracing over E the system/environment entangled state.
A surprising corollary of this line of argument is the realization (Zurek and Paz 1994) that the dynamical second law – entropy production at the scale set by the dynamics of the system and more or less independent of the strength of the coupling to the environment – is a natural and, indeed, an inevitable consequence Decoherence and the Transition from Quantum to Classical – Revisited 23 of decoherence. This point has been since confirmed in numerical studies (Miller and Sarkar 1999, Pattanayak 1999, Monteoliva and Paz 2000).
Rev. D. 40, 1071 (1989). [61] 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. [62] J. A. Wheeler, Assessment of Everett’s “Relative State” Formulation of Quantum Theory, Rev. Mod. Phys. 29, 463 (1957). [63] —, Information, Physics, Quantum: The Search for Links, In Complexity, Entropy, and the Physics of Information. p. 3. Edited by W.
Quantum Decoherence. Poincare Seminar by Duplantier B., Raimond J.-M., Rivasseau V.
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