Evolution of Liouville density of a chaotic system
chao-dyn
2009-10-28 v1 Chaotic Dynamics
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 Schr\"odinger wave function which requires, for the analogous quantum system, a basis of fixed size.
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Cite
@article{arxiv.chao-dyn/9505014,
title = {Evolution of Liouville density of a chaotic system},
author = {Asher Peres and Daniel Terno},
journal= {arXiv preprint arXiv:chao-dyn/9505014},
year = {2009}
}
Comments
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