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arXiv:quant-ph/0402176 · The European Physical Journal B

Loss of quantum coherence in a system coupled to a zero-temperature environment

Alexandre Ratchov, Fréderic Faure, F. W. J. Hekking

Published Aug 1, 2005• 13 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2005-00284-2

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Interaction between a quantum system and its environment can be often regarded as a measurement, in the course of which one of the system observables influences the evolution of the external degrees of freedom and is thus monitored'' by the environment. This causes the system to decohere.'' Loss of quantum coherence erases part of the density matrix responsible for the correlations between the eigenstates of the monitored observables. This mechanism is very efficient even in the limit of weak coupling to the environment. The classical limit of quantum theory -- that is, both classical irreversible equations of motion and classical states (trajectories in phase space rather than their superpositions) obtains in the limit in which the coupling strength and the Planck constant simultaneously tend to zero. Transition from quantum to classical in the inflationary cosmological model can be justified in the framework of environment induced susperselection. 24 refs., 2 figs.
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Interaction between a quantum system and its environment can be often regarded as a measurement, in the course of which one of the system observables influences the evolution of the external degrees of freedom and is thus ''monitored'' by the environment. The resulting loss of quantum coherence erases part of the density matrix responsible for the correlations between the eigenstates of the monitored observable. This mechanism is very efficient even in the limit of weak coupling. Indeed, the classical limit of quantum theory---that is, both classically reversible equations of motion and classical states (trajectories in phase space rather than their superpositions) can be naturally attained when both the coupling strength and the Planck constant simultaneously tend to zero. Transition from quantum to classical in the inflationary cosmological models can be justified in the framework of environment induced superselection. 24 refs., 3 figs.