Critical bending point in the Lyapunov localization spectra of many-particle systems

Details Critical bending point in the Lyapunov localization spectra of many-particle systems Critical bending point in the Lyapunov localization spectra of many-particle systems

2005-02-16

arxiv.org/abs/nlin/0502032v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures

Scientific paper

The localization spectra of Lyapunov vectors in many-particle systems at low density exhibit a characteristic bending behavior. It is shown that this behavior is due to a restriction on the maximum number of the most localized Lyapunov vectors determined by the system configuration and mutual orthogonality. For a quasi-one-dimensional system this leads to a predicted bending point at n_c \approx 0.432 N for an N particle system. Numerical evidence is presented that confirms this predicted bending point as a function of the number of particles N.

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