Breathers on lattices with long range interaction

TL;DR

This paper investigates breathers in lattices with long-range interactions, revealing a crossover from exponential to algebraic decay and analyzing energy thresholds depending on the decay parameter s.

Contribution

It provides a detailed analysis of how long-range interactions affect breather decay properties and energy thresholds, extending previous short-range results to algebraically decaying interactions.

Findings

Breather decay transitions from exponential to algebraic with distance.

Energy thresholds depend on the decay exponent s, with a critical value at s=3.

For s<3, nonzero energy thresholds occur even where short-range systems have zero thresholds.

Abstract

We analyze the properties of breathers (time periodic spatially localized solutions) on chains in the presence of algebraically decaying interactions $1/r^s$. We find that the spatial decay of a breather shows a crossover from exponential (short distances) to algebraic (large distances) decay. We calculate the crossover distance as a function of $s$ and the energy of the breather. Next we show that the results on energy thresholds obtained for short range interactions remain valid for $s>3$ and that for $s < 3$ (anomalous dispersion at the band edge) nonzero thresholds occur for cases where the short range interaction system would yield zero threshold values.