Decoherence and the quantum-classical limit in the presence of chaos

Abstract

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 $\chi$ that relates an effective Planck constant ${\hslash }_{\mathrm{eff}}$, the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on ${\hslash }_{\mathrm{eff}}$, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for $\chi \lesssim 1$, the separation remains small, going down with ${\hslash }_{\mathrm{eff}}^2$, so the concept of separation time loses its meaning.

5 pages, 4 figures (in 6 postscript files) two of them are color figures

References in corpus (1)

• Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator

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• Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians