Characteristics of Quantum-Classical Correspondence for Two Interacting Spins

Abstract

The conditions of quantum-classical correspondence for a system of two interacting spins are investigated. Differences between quantum expectation values and classical Liouville averages are examined for both regular and chaotic dynamics well beyond the short-time regime of narrow states. We find that quantum-classical differences initially grow exponentially with a characteristic exponent consistently larger than the largest Lyapunov exponent. We provide numerical evidence that the time of the break between the quantum and classical predictions scales as log($\mathcal{J}/\hslash$), where $\mathcal{J}$ is a characteristic system action. However, this log break-time rule applies only while the quantum-classical deviations are smaller than order hbar. We find that the quantum observables remain well approximated by classical Liouville averages over long times even for the chaotic motions of a few degree-of-freedom system. To obtain this correspondence it is not necessary to introduce the decoherence effects of a many degree-of-freedom environment.

New introduction, accepted in Phys Rev A (May 2001 issue), 12 latex figures, 3 ps figures

References in corpus (2)

• Decoherence, Chaos, and the Correspondence Principle
• Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time

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