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Evolution of Liouville density of a chaotic system

Asher Peres·Daniel Terno
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Abstract

An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially necessitates only a finite number of basis functions. As the dynamical mapping proceeds, it is found that the number of non-negligible coefficients increases exponentially with the number of steps. This is to be contrasted with the behavior of a Schrödinger wave function which requires, for the analogous quantum system, a basis of fixed size.

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BibTeXRIS

Asher Peres, Daniel Terno. 1995-05-31. Evolution of Liouville density of a chaotic system. https://doi.org/10.1103/physreve.53.284

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