Non-linear Dynamical Excitations in Solids

Vibrational excitations can exist in non-linear systems which have no counterpart in the corresponding linear systems. In this paper we investigate such excitations in systems where the non-linearity is of an on-site character. In particular, we analyze the existence conditions for localized (and delocalized) excitations, and their interaction with external fields. In this paper we discuss the properties of non-linear periodic lattice waves in models of perfect and imperfect crystals. Our model Hamiltonians contain a fourth-order on-site electron-ion potential+ reminiscent of I$~-models. This approach is motivated by the success of the self-consistent phonon approximation (SPA) for the investigations of ferroelectric-type phase transitions in terms of such models (refer to Bussmann et al., this Conference). 2. General Solution to the Dynamical Monomer Problem The monomer (Fig. 1 ) consists of one anion and one cation. If the center of mass motion is factored out, the system is described by two coupled variables, which may be chosen as the displacement, u, of the cation relative to the anion core and the displacement, w, of the anion shell relative to its core. The oscillation frequency of the monomer is displayed in Fig. 2 as a function of wg, where wo is the maximum dis2 2 placement from the origin. The range w >wcrit 0 Fig. 1 The monaner unit.g4 belongs to anharmonic oscillations which tra2 IS the fourth Order verse the origin w=o (the solution at wo=O. 4 constant. is the only harmonic one). The range w : describes oscillations which are localized in one or another of two equivalent potential wells. The minimum squared displacement from the 2 origin increases from zero to the left of wCrit until it coincides with W : at -g2/g4 (notice that the frequency does not go to zero at this point). "Permanent address : Department of Physics, University of California, Irvine, CA 92717, U.S.A. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981641