Renormalized waves and discrete breathers in $\beta$-FPU chains

TL;DR

This paper shows that in the strongly nonlinear regime, the $eta$-FPU chain behaves like weakly nonlinear waves due to renormalization, with localized discrete breathers coexisting with extended waves.

Contribution

It introduces the concept of renormalized waves in strongly nonlinear $eta$-FPU chains and reveals their weakly nonlinear behavior and localized breather dynamics.

Findings

Strong nonlinear interactions effectively renormalize linear dispersion.

Thermalized chains exhibit localized discrete breathers.

Renormalized waves behave like weakly nonlinear waves.

Abstract

We demonstrate via numerical simulation that in the \textit{strongly} nonlinear limit, the $\beta$-FPU system in thermal equilibrium behaves surprisingly like weakly nonlinear waves in properly renormalized normal variables. This arises because the collective effect of strongly nonlinear interactions effectively renormalizes linear dispersion frequency and leads to effectively weak interaction among these renormalized waves. Furthermore, we show that the dynamical scenario for thermalized $\beta$-FPU chains is spatially highly localized discrete breathers riding chaotically on spatially extended, renormalized waves.