Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems

Abstract

The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed in two types of Lyapunov modes, one associated with the time translational invariance and another with the spatial translational invariance, and their phase relation is specified. It is shown that the longest period of the Lyapunov modes is twice as long as the period of the longitudinal momentum auto-correlation function. A simple explanation for this relation is proposed. This result gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.

4 pages, 3 figures

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• Critical bending point in the Lyapunov localization spectra of many-particle systems
• Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices
• Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems
• On the angle between the first and the second Lyapunov vectors in spatio-temporal chaos
• Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems
• Escape Dynamics of Many Hard Disks