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arXiv:quant-ph/0111002 · Physical Review Letters

Quantum Chaotic Environments, the Butterfly Effect, and Decoherence

Zbyszek P. Karkuszewski, Christopher Jarzynski, Wojciech Hubert Zurek

Published Oct 8, 2002• 131 citations
arXivHTMLPDF

Abstract

We investigate the sensitivity of quantum systems that are chaotic in a classical limit to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to decoherence when the environment has a chaotic classical counterpart.
DOI
10.1103/physrevlett.89.170405

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We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model. For a wide range of parameters, the distance between the corresponding phase-space distributions depends on a single parameter $\ensuremath{\chi}$ that relates an effective Planck constant ${\ensuremath{\hbar}}_{\mathrm{eff}}$, the Lyapunov coefficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on ${\ensuremath{\hbar}}_{\mathrm{eff}}$, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for $\ensuremath{\chi}\ensuremath{\lesssim}1$, the separation remains small, going down with ${\ensuremath{\hbar}}_{\mathrm{eff}}^{2}$, so the concept of separation time loses its meaning.