Fractional and split crowdions in complex crystal structures

An analysis is made of the existence conditions and dynamical features of c rowdion excitations in crystals with a complex structure of the crystalline field forming the crowdions in close-packed atomic rows. The crystalline m atrix is assumed to be absolutely rigid, and the description of the crowdio ns therefore reduces to analysis of the generalized Frenkel-Kontorova model and the Klein-Gordon nonlinear differential equation corresponding to it. The cases of the so-called double-well and double-barrier potentials of the crystalline field are studied in this model: the structures of subcrowdion s with fractional topological charges and of split whole crowdions are desc ribed, as is the asymptotic decay of split crowdions into subcrowdions when the double-barrier potential is transformed into a double well. The existe nce conditions of special types of subcrowdions are discussed separately; t hese conditions involve the atomic viscosity of the crystal and the externa l force applied to it. The qualitative analysis presented does not presuppo se an exact solution of the Klein-Gordon nonlinear equation in explicit for m. The results of this study generalize the conclusions reached previously in a study of certain particular cases of exactly solvable Klein-Gordon equ ations with complex potentials. The results of this study may be used not o nly in the physics of crowdions but also in other branches of nonlinear phy sics based on the Frenkel-Kontorova model. (C) 2001 American Institute of P hysics.