Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems
arXiv:nlin/0506060 · doi:10.1103/PhysRevE.73.036208
Abstract
The dynamics of the localized region of the Lyapunov vector for the largest Lyapunov exponent is discussed in quasi-one-dimensional hard-disk systems at low density. We introduce a hopping rate to quantitatively describe the movement of the localized region of this Lyapunov vector, and show that it is a decreasing function of hopping distance, implying spatial correlation of the localized regions. This behavior is explained quantitatively by a brick accumulation model derived from hard-disk dynamics in the low density limit, in which hopping of the localized Lyapunov vector is represented as the movement of the highest brick position. We also give an analytical expression for the hopping rate, which is obtained us a sum of probability distributions for brick height configurations between two separated highest brick sites. The results of these simple models are in good agreement with the simulation results for hard-disk systems.
28 pages, 13 figures
References in corpus (13)
- Goldstone modes in Lyapunov spectra of hard sphere systems
- Lyapunov instabilities of Lennard-Jones fluids
- Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems
- Lyapunov Modes in Hard-Disk Systems
- Stepwise structure of Lyapunov spectra for many particle systems by a random matrix dynamics
- Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems
- Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems
- Hard Disks in Narrow Channels
- Lyapunov spectra of periodic orbits for a many-particle system
- Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
- Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems
- Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases
- A numerical study of the development of bulk scale-free structures upon growth of self-affine aggregates