Optical-acoustical interaction in FPU-chains with alternating large masses (plus appendix)

TL;DR

This paper investigates optical-acoustical interactions in FPU-chains with alternating large masses, revealing significant interactions in alpha-chains under external forcing and negligible interactions in beta-chains with parametric forcing.

Contribution

It provides a detailed analysis of how optical and acoustical modes interact in specific FPU-chain configurations, highlighting the effects of external and parametric forcing.

Findings

Significant optical-acoustical interactions in alpha-chains with external forcing.

Negligible interactions in beta-chains with parametric forcing.

Interaction strength depends on chain type and forcing method.

Abstract

One of the problems of periodic FPU-chains with alternating masses is whether significant interactions exist between the so-called (high frequency) optical and (low frequency) acoustical groups. We show that for $\alpha$-chains with $4n$ and $8n$ particles ($n= 1, 2, \ldots$) we have significant interactions caused by external forcing. For $\beta$-chains with $4$ and $8$ particles the interactions are characterised by parametric forcing, the interactions are negligible.