Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-sites breathers, the methods for determining the stability properties of multibreathers rely in numerical computation of the Floquet multipliers or in the weak nonlinearity approximation leading to discrete non-linear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides with a simple method to determine multibreathers stability in Klein-Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry's band theory. We illustrate them with several examples.

No abstract

Reaction rate theory in solids is modified taking into account intrinsic localized modes or discrete breathers (DBs) that can appear in crystals with sufficient anharmonicity, resulting in violation of Arrhenius' law. Largeamplitude oscillations of atoms about their equilibrium positions in the lattice cause local potentials of alternating sign, which are described in terms of time-periodic modulations of the potential barriers for chemical reactions taking place in the vicinity of DBs. The reaction rate averaged over large macroscopic volumes and times including many DBs is increased by a factor that depends on the DB statistics. The breather statistics in thermal equilibrium and in thermal spikes in solids under irradiation with swift particles is considered, and the corresponding reaction rate amplification factors are derived.

Reconstructive transformations in layered silicates need a high temperature in order to be observed. However, very recently, some systems have been found where transformation can be studied at temperatures 600 degrees C below the lowest experimental results previously reported, including sol-gel methods. We explore the possible relation with the existence of intrinsic localized modes, known as discrete breathers. We construct a model for nonlinear vibrations within the cation layer, obtain their parameters, and calculate them numerically, obtaining their energies. Their statistics show that, although there are far less breathers than phonons, there are much more above the activation energy, making them good candidates to explain the reconstructive transformations at low temperatures.

We analyze the influence of an impurity in the movement of discrete breathers in Klein-Gordon chains. We observe that the moving breather can cross the impurity, can be reflected by it, or can be trapped originating a quasi-periodic breather. We find that resonance with a nonlinear localised mode centred in the impurity is a necessary condition in order to observe the trapping phenomenon, as a difference with the resonance condition with a linear localised mode when this problem is studied within the Nonlinear Schrödinger Equation approximation.