Hamilton-Jacobi formulation of Kolmogorov-Sinai entropy for classical and quantum dynamics |
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Authors: | Partovi M Hossein |
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Institution: | Department of Physics and Astronomy, California State University, Sacramento, California 95819-6041, USA. hpartovi@csus.edu |
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Abstract: | A Hamilton-Jacobi formulation of the Lyapunov spectrum and Kolmogorov-Sinai (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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