Course 8: Environment-Induced Decoherence and the Transition from Quantum to Classical

Juan Pablo Paz, Wojciech Hubert Zurek

Wojciech Hubert Zurek

J. P. Paz, W. H. Zurek

Wojciech Hubert Zurek

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.

Juan Pablo Paz, Augusto J. Roncaglia

We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model, we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced classicality. To study this, we present a measure of redundancy and compare it to the existing one.

Wojciech Hubert Zurek

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.