Time-oscillating Lyapunov modes and the momentum autocorrelation function

Area of Science:

• * Statistical mechanics
• * Nonlinear dynamics
• * Condensed matter physics

Background:

• * Many-particle systems exhibit complex dynamics governed by Lyapunov spectra.
• * Lyapunov vectors reveal system sensitivity to initial conditions.
• * Understanding Lyapunov modes is crucial for characterizing system behavior.

Purpose of the Study:

• * To investigate the time-oscillating behavior of Lyapunov vectors in many-particle systems.
• * To establish a quantitative relationship between Lyapunov modes and experimentally measurable quantities.
• * To provide a theoretical explanation for observed periodicities in Lyapunov modes.

Main Methods:

• * Analysis of Lyapunov vectors and spectra for many-particle systems.
• * Examination of time-translational and spatial-translational invariance in Lyapunov modes.
• * Calculation and comparison of periods for Lyapunov modes and momentum autocorrelation functions.

Main Results:

• * Two types of Lyapunov modes were identified: time-translational and spatial-translational.
• * The longest period of Lyapunov modes was found to be twice the period of the momentum autocorrelation function for each coordinate direction.
• * A simple explanation for this observed relationship was proposed.

Conclusions:

• * A general relationship between Lyapunov modes and momentum autocorrelation functions in many-particle systems has been established.
• * This finding provides the first quantitative link between Lyapunov modes and experimentally accessible quantities.
• * The results offer new insights into the dynamics and characterization of many-particle systems.