Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

Details Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

2003-04-15

arxiv.org/abs/nlin/0304028v1

Phys. Rev. E 68, 046203 (2003)

Nonlinear Sciences

Chaotic Dynamics

41 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/R

Scientific paper

10.1103/PhysRevE.68.046203

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of particle contributions, a delocalization associated with a uniform distribution and a delocalization associated with a wave-like structure in the Lyapunov vector. Using the localization width we show that in quasi-one-dimensional systems of many hard disks there are two kinds of dependence of the localization width on the Lyapunov exponent index for the larger exponents: one is exponential, and the other is linear. Differences, due to these kinds of localizations also appear in the shapes of the localized peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the spatial and momentum parts of the Lyapunov vectors. We show that the Krylov relation for the largest Lyapunov exponent $\lambda\sim-\rho\ln\rho$ as a function of the density $\rho$ is satisfied (apart from a factor) in the same density region as the linear dependence of the localization widths is observed. It is also shown that there are asymmetries in the spatial and momentum parts of the Lyapunov vectors, as well as in their $x$ and $y$-components.

Affiliated with

Also associated with

No associations

Rating

Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-478259