Unusual slow energy relaxation induced by mobile discrete breathers in one-dimensional lattices with next-nearest-neighbor coupling

TL;DR

This paper investigates how mobile discrete breathers in one-dimensional lattices with next-nearest-neighbor coupling cause unusual slow energy relaxation, revealing universal and system-dependent relaxation behaviors through numerical analysis.

Contribution

It uncovers the role of mobile discrete breathers in slow energy relaxation and identifies universal relaxation crossovers influenced by breather-phonon interactions.

Findings

Two relaxation crossovers: from stretched-exponential to exponential, then to power-law.

Power-law relaxation is faster in FPUT-$\beta$ systems due to breather scattering.

Universal initial relaxations, system-specific long-term decay behaviors.

Abstract

We study the energy relaxation process in one-dimensional (1D) lattices with next-nearest-neighbor (NNN) couplings. This relaxation is produced by adding damping (absorbing conditions) to the boundary (free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers (DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e., these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi-Pasta-Ulam-Tsingou-$\beta$ (FPUT-$\beta$) types, we find two crossovers of relaxation in general, i.e., a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-$\beta$ type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices.