Chaos and thermalization in a classical chain of dipoles

TL;DR

This study investigates how chaos and energy localization influence thermalization in a classical chain of dipoles, revealing that chaotic breathers can prevent ergodicity and affect energy distribution.

Contribution

It demonstrates the role of chaotic breathers in delaying ergodicity and links participation ratio to thermal equilibrium in a classical dipole chain.

Findings

Chaotic behavior correlates with energy localization and ergodicity.

Chaotic breathers hinder energy equipartition and ergodicity.

Participation ratio indicates approach to thermal equilibrium.

Abstract

We explore the connection between chaos, thermalization and ergodicity in a linear chain of $N$ interacting dipoles. Starting from the ground state, and considering chains of different numbers of dipoles, we introduce single site excitations with energy $\Delta K$. The time evolution of the chaoticy of the system and the energy localization along the chain is analyzed by computing, up to very long times, the statistical average of the finite time Lyapunov exponent $\lambda(t)$ and of the participation ratio $\Pi(t)$. For small $\Delta K$, the evolution of $\lambda(t)$ and $\Pi(t)$ indicates that the system becomes chaotic at roughly the same time as $\Pi(t)$ reaches a steady state. For the largest values of $\Delta K$, the system becomes chaotic at an extremely early stage in comparison with the energy relaxation times. We find that this fact is due to the presence of chaotic breathers that keep the system far from equipartition and ergodicity. Finally, we show that the asymptotic values attained by the participation ratio $\Pi(t)$ fairly corresponds to thermal equilibrium.