Dynamics of strongly localized Lyapunov vectors in many-hard-disk systems.
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 the Lyapunov vector, and show that it is a decreasing function of the hopping distance, implying a 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 as 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.
Taniguchi
Tooru
T
School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia.
Morriss
Gary P
GP