Chaotic dynamics of a one-dimensional Coulomb system with periodic boundary conditions

Abstract

Simulation tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions are provided. Results of a simulation study of the nonlinear dynamics and the thermodynamics of a spatially-periodic single-component one-dimensional Coulomb system are reported. Analytic expressions are derived for the electric potential and field using Ewald sums and the resulting equations of motions are utilized to follow the exact time-evolution of the system using an event-driven algorithm. For a system of three particles, Poincare maps are plotted and the largest Lyapunov exponents are calculated. The results indicate that the three-particle system exhibits interesting dynamics with the phase-space containing periodic, quasiperiodic, as well as chaotic regions for different initial conditions. Simulation results in the thermodynamic limit indicate that the net pressure is equal to the kinetic pressure for all temperatures and there is no phase transition.