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

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

2001-07-16

arxiv.org/abs/quant-ph/0107083v1

Phys. Rev. Lett. 89, 144101 (2002)

Physics

Quantum Physics

preprint, 8 pages (revtex)

Scientific paper

10.1103/PhysRevLett.89.144101

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.

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