Mobility and Reactivity of Discrete Breathers

TL;DR

This paper investigates the mobility and reactivity of discrete breathers, revealing how marginal modes at instability thresholds influence their movement and interactions, with implications across physics and chemistry.

Contribution

It introduces the concept of marginal modes affecting breather mobility and reactions, providing a new perspective on their behavior near instability thresholds.

Findings

Exact mobile breather solutions with extended tails are found numerically.

Breather reactions include fission and fusion driven by marginal modes.

Breather behavior parallels reactions in chemistry and nuclear physics.

Abstract

Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in time. In some cases, there are exact mobile breather solutions (found numerically), but these solutions have an infinitely extended tail which shows that the breather motion is nonradiative only when it moves (in equilibrium) with a particular phonon field. More generally, at any instability threshold, there is a marginal mode. There are situations where excitations by marginal modes produce new type of behaviors such as the fission of a breather. We may also have fusion. This approach suggests that breathers (which can be viewed as cluster of phonons) may react by themself or one with each others as well as in chemistry for atoms and molecules, or in nuclear physics for nuclei.