Discrete breathers in crystals

Abstract

It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite definitive evidence for the existence of DBs in crystals, their role in solid-state physics remains unclear. This review addresses some of the problems that are specific to real crystal physics and which went undiscussed in the classical literature on DBs. In particular, the interaction of a moving DB with lattice defects is examined, the effect of elastic lattice deformations on the properties of DBs and the possibility of their existence are discussed, and recent studies of the effect of nonlinear lattice perturbations on the crystal electron subsystem are presented.