Discrete breathers in crystals: achievements and open problems

Abstract

It has long been known that periodic discrete systems containing defects, in addition to traveling waves, allow for the existence of vibrational modes localized on defects. It turned out that if a periodic discrete system is nonlinear, it can support exact solutions in the form of spatially localized vibrational modes even in the absence of defects. Since all the nodes of the system are identical, only a special choice of initial conditions can distinguish the group of nodes, on which such localized mode, called discrete breather (DB), will be excited. Frequency of DB must lie outside the spectrum of small-amplitude traveling waves. Do not resonating with traveling waves and do not losing energy to their excitation, theoretically DB can maintain its vibrational energy forever, in the absence of thermal vibrations and other perturbations. Crystals are nonlinear discrete systems and discovery of DB in them was only a matter of time. Experimental studies of DB run into considerable technical difficulties, and the main tool of their study is by far the atomistic computer simulations. Having gained confidence in the existence of DB in crystals, we still poorly understand their role in solid state physics. This review covers issues specific to the physics of real crystals, which were not considered in the classical works on DB. In particular, it discusses the interaction of moving DB with crystal lattice defects, analyzes the influence of the elastic deformation of the lattice on the DB properties, presents recent works on the effect of nonlinear lattice excitations on the electron subsystem of the crystal, etc.

Mechanical properties of fullerite of various composition

“…This part of the AIREBO potential is used to describe the pairwise Van der Waals interatomic forces between the structural elements (fullerenes). This potential is based on the well-known Tertsoff potential, and have been actively used to study carbon structures and widely used to study various carbon structures and their properties [47][48][49][50][51][52][53]. Equations of motion of atoms were integrated according to the Verle method of the fourth order of accuracy with an integration step of 0.2 fs.…”

Graphane -- material for hydrogen storage, breathers and kinks

“…The author obtains sufficient conditions for the existence of such solutions. Dmitriev [7] discusses discrete breathers in crystals. An overview of the dynamics of the Frenkel-Kontorova model, is presented in [8].The model describes the motion of a chain of interacting particles subjected to an external on-site periodic potential.…”