2003/04/15 by Tooru Taniguchi, Gary P. Morriss · 4 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Theoretical and Computational Physics #nlin.CD
paper · pdf · doi:10.1103/physreve.68.046203
published as Phys. Rev. E 68, 046203 (2003) · 41 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/Research.html
arxiv created 2003/04/15 · openalex publication_date 2003/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 wavelike 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 approximately -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.