Localization and Equipartition of Energy in the beta-FPU Chain : Chaotic Breathers

TL;DR

This paper investigates how energy localizes and spreads in the beta-FPU chain, revealing the formation of chaotic breathers that efficiently collect and transport energy, with their lifetime linked to system energy density.

Contribution

It demonstrates the existence of chaotic breathers in the beta-FPU chain, connecting their dynamics to Lyapunov and Floquet spectra, and identifies their role in energy equipartition.

Findings

Chaotic breathers form above an energy threshold.

Their lifetime depends on the energy density, diverging as epsilon approaches zero.

They efficiently transport large amounts of energy across the chain.

Abstract

The evolution towards equipartition in the $\beta$-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally unstable and to give rise to a striking localization process. The spontaneously created excitations have strong similarity with moving exact breathers solutions. But they have a finite lifetime and their dynamics is chaotic. These chaotic breathers are able to collect very efficiently the energy in the chain. Therefore their size grows in time and they can transport a very large quantity of energy. These features can be explained analyzing the dynamics of perturbed exact breathers of the FPU chain. In particular, a close connection between the Lyapunov spectrum of the chaotic breathers and the Floquet spectrum of the exact ones has been found. The emergence of chaotic breathers is convincingly explained by the absorption of high frequency phonons whereas a breather's metastability is for the first time identified. The lifetime of the chaotic breather is related to the time necessary for the system to reach equipartition. The equipartition time turns out to be dependent on the system energy density $\epsilon$ only. Moreover, such time diverges as $\epsilon^{-2}$ in the limit $\epsilon \to 0$ and vanishes as $\epsilon^{-1/4}$ for $\epsilon \to \infty$.