Lyapunov spectra of Coulombic and gravitational periodic systems

TL;DR

This paper computes Lyapunov spectra for one-dimensional Coulombic and gravitational systems with periodic boundary conditions, revealing energy-dependent chaotic behavior and providing a tool for studying thermodynamic transitions.

Contribution

It introduces an exact, event-driven method for calculating Lyapunov spectra in these systems, enabling detailed dynamical analysis without approximations.

Findings

Largest Lyapunov exponent correlates with Kolmogorov-entropy density.

Method effectively studies thermodynamic transitions in large periodic systems.

Results highlight energy dependence of chaos in Coulombic and gravitational systems.

Abstract

We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward computing Lypaunov characteristic exponents using an event-driven algorithm. The results indicate that the energy dependence of the largest Lyapunov exponent emulates that of Kolmogorov-entropy density for each system at different degrees of freedom. Our approach forms an effective and approximation-free tool toward studying the dynamical properties exhibited by the Coulombic and gravitational systems and finds applications in investigating indications of thermodynamic transitions in large versions of the spatially periodic systems.