Dynamical Fluctuations of Observables and the Ensemble of Classical Trajectories

概要

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The long term behavior of non-integrable quantum systems is investigated to find a classical counterpart that describes the statistical properties of dynamical fluctuation of quantum observables. On the basis of the quantum-classical correspondence in the integrable system, we introduce the ensemble of classical trajectories (ECT), which is defined as a set of weighted classical trajectories whose mean density in phase space is one per Planck cell. In the non-integrable system, due to the rapid breakdown of quantum-classical correspondence of the wavepacket dynamics, the ECT is unable to yield the correct temporal behavior of quantum observables. However, numerical experiments reveal that it gives a good approximation of various statistical properties of the quantum dynamical fluctuation. This result strongly suggests that, as far as the statistical properties are concerned, the dominant part of the quantum dynamical fluctuation is determined by classical dynamics, i.e. a set of classical trajectories. The meaning and interpretation of the ECT in relation to the coherent subsystem is also discussed.
一般社団法人日本物理学会の論文
1993-08-15