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

F. Toscano·R. L. de Matos Filho·L. Davidovich
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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 $χ$ that relates an effective Planck constant $\hbar_{\rm eff}$, the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a time that depends logarithmically on $\hbar_{\rm eff}$, in agreement with previous estimations of the separation time for Hamiltonian systems. However, for $χ\lesssim 1$, the separation remains small, going down with $\hbar_{\rm eff}^2$, so the concept of separation time loses its meaning.

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F. Toscano, R. L. de Matos Filho, L. Davidovich. 2004-10-19. Decoherence and the quantum-classical limit in the presence of chaos. https://doi.org/10.1103/physreva.71.010101

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