Stepwise structure of Lyapunov spectra for many particle systems by a random matrix dynamics

Abstract

The structure of Lyapunov spectra for many particle systems with a random interaction between the particles is discussed. The dynamics of the tangent space is expressed as a master equation, which leads to a formula that connects the positive Lyapunov exponents and the time correlations of the particle interaction matrix. Applying this formula to one and two dimensional models we investigate the stepwise structure of the Lyapunov spectra, which appear in the region of small positive Lyapunov exponents. Long range interactions lead to a clear separation of the Lyapunov spectra into a part exhibiting stepwise structure and a part changing smoothly. The part of the Lyapunov spectrum containing the stepwise structure is clearly distinguished by a wave like structure in the eigenstates of the particle interaction matrix. The two dimensional model has the same step widths as found numerically in a deterministic chaotic system of many hard disks.

arXiv comment15 pages, 6 figures

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Cited by in corpus (15)

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• Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems
• Covariant Lyapunov vectors for rigid disk systems
• Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems
• Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
• Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems
• What does dynamical systems theory teach us about fluids?
• Lyapunov Modes for a Nonequilibrium System with a Heat Flux
• Lyapunov Mode Dynamics in Hard-Disk Systems
• From Lyapunov modes to the exponents for hard disk systems
• Critical bending point in the Lyapunov localization spectra of many-particle systems
• Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems
• Lyapunov modes in three-dimensional Lennard-Jones fluids