Delocalization transition of a small number of particles in a box with periodic boundary conditions

TL;DR

This study uses molecular dynamics to explore how a small number of particles transition from confined to chaotic diffusion states in a periodic box, revealing anomalous jump behaviors near a critical energy.

Contribution

It uncovers the nature of the delocalization transition and the associated anomalous jump frequency behavior in small particle systems with periodic boundary conditions.

Findings

Transition at critical energy E_c from confinement to chaos

Anomalous jump frequency behavior above E_c in two-particle systems

Simultaneous jump motions in multi-particle systems near E_c

Abstract

We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a view point of chaotic dynamical systems. There is a transition at a critical energy E_c that each particle is confined in each unit cell for E<E_c, and the chaotic diffusion occurs for E>E_c. We find an anomalous behavior of the jump frequency above the critical energy in a two-particle system, which is related with the infinitely alternating stability change of the straight motion passing through a saddle point. We find simultaneous jump motions just above the critical energy in a four-particle system and sixteen-particle system, which is also related with the motion passing through the saddle point.