Hamilton-Jacobi Formulation of KS Entropy for Classical and Quantum Dynamics

Abstract

A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum domain using the Madelung-Bohm orbits associated with the Schroedinger equation. The resulting quantum KS invariant for a given orbit equals the mean decay rate of the probability density along the orbit, while its ensemble average measures the mean growth rate of configuration-space information for the quantum system.

preprint, 8 pages (revtex)

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• Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
• Exponential mixing and log h time scales in quantized hyperbolic maps on the torus
• An Entire Spectral Determinant for Semiclassical Quantization

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