$q$-Breathers in the diatomic $\beta$-Fermi-Pasta-Ulam- Tsingou chains

TL;DR

This paper investigates $q$-Breathers in diatomic Fermi-Pasta-Ulam-Tsingou chains, deriving analytical stability thresholds, and demonstrates how bandgap effects influence energy localization and thermalization in nonlinear lattices.

Contribution

It provides the first analytical expression for QB instability thresholds in diatomic chains and explores how bandgap size affects QB stability and energy localization.

Findings

Analytical instability thresholds derived for low-frequency QBs.

Bandgap presence enhances QB stability.

Thresholds depend inversely on system size and quadratically on mass difference.

Abstract

$q$-Breathers (QBs) represent a quintessential phenomenon of energy localization, manifesting as stable periodic orbits exponentially localized in normal mode space. Their existence can hinder the thermalization process in nonlinear lattices. In this study, we employ the Newton's method to identify QB solutions in the diatomic Fermi-Pasta-Ulam-Tsingou chains and perform a comprehensive analysis of their linear stability. We derive an analytical expression for the instability thresholds of low-frequency QBs, which converges to the known results of monoatomic chains as the bandgap approaches zero. The expression reveals an inverse square relationship between instability thresholds and system size, as well as a quadratic dependence on the mass difference, both of which have been corroborated through extensive numerical simulations. Our results demonstrate that the presence of a bandgap can markedly enhance QB stability, providing a novel theoretical foundation and practical framework for controlling energy transport between modes in complex lattice systems. These results not only expand the applicability of QBs but also offer significant implications for understanding the thermalization dynamics in complex lattice structures, with wide potential applications in related low-dimensional materials.