Stepwise structure of Lyapunov spectra for many particle systems by a random matrix dynamics
Abstract
The structure of Lyapunov spectra for many particle systems with a random interaction between the particles is discussed. The dynamics of the tangent space is expressed as a master equation, which leads to a formula that connects the positive Lyapunov exponents and the time correlations of the particle interaction matrix. Applying this formula to one and two dimensional models we investigate the stepwise structure of the Lyapunov spectra, which appear in the region of small positive Lyapunov exponents. Long range interactions lead to a clear separation of the Lyapunov spectra into a part exhibiting stepwise structure and a part changing smoothly. The part of the Lyapunov spectrum containing the stepwise structure is clearly distinguished by a wave like structure in the eigenstates of the particle interaction matrix. The two dimensional model has the same step widths as found numerically in a deterministic chaotic system of many hard disks.
Keywords
Cite
@article{arxiv.nlin/0112024,
title = {Stepwise structure of Lyapunov spectra for many particle systems by a random matrix dynamics},
author = {Tooru Taniguchi and Gary P. Morriss},
journal= {arXiv preprint arXiv:nlin/0112024},
year = {2007}
}
Comments
15 pages, 6 figures