Mobility and Reactivity of Discrete Breathers

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.