BOUNDARY-CONDITION EFFECTS IN ANHARMONIC LATTICE-DYNAMICS - EXISTENCECRITERIA FOR INTRINSIC LOCALIZED MODES FROM EXTENDED-MODE PROPERTIES

Recent theoretical studies of periodic one-dimensional anharmonic latt ices with standard periodic boundary conditions established fundamenta l connections between the existence of intrinsic localized modes (ILM' s) and the stability of the extended lattice modes into which they evo lve with decreasing amplitude. While the odd-order anharmonicity drops out of the equations of motion far the extended modes within these bo undary conditions, it nevertheless produces an amplitude-dependent per iod-averaged ''dynamical stress'' across the supercell boundaries. Her e, we allow the supercell length to adjust so as to eliminate this str ess and find that the frequency vs amplitude curves for the anharmonic extended modes are markedly changed for a variety of realistic neares t-neighbor interactions, whereas highly localized ILM's are little aff ected. Nevertheless, in all cases ILM existence remains intimately con nected to an instability of the associated extended mode. Furthermore, the use of zero-stress periodic boundary conditions now allows one to predict the spatial extent of an ILM from extended-mode stability pro perties in lattices with odd-order anharmonicity. Most importantly, fo r the zero-stress periodic boundary conditions we obtain an additional ILM existence criterion, based on simple dynamical properties of the unperturbed related extended mode. Since well-localized ILMs are indep endent of the specific choice of boundary conditions, our results yiel d promising tools for ILM predictions in real systems.