ONE-PARTICLE INTERACTING WITH THE ACOUSTICAL PHONONS IN A DISCRETE CHAIN

We have applied a variational method to study both the Davydov model a nd the Su, Schrieffer, and Heeger model for the interaction between an electron and the acoustical phonons of a discrete chain. A class of l ocalized solutions has been found for both of these models. These solu tions appear in the intermediate values of the adiabaticity gamma simi lar to 1 when the particle-phonon coupling constant lambda is near the critical point for the delocalization-localization transition. We hav e widely discussed the limits of the continuum approximation, stressin g the importance of the application of the method to a discrete system if we want to explore the transition from a large mobile polaron to a strong localized heavy polaron. Furthermore, we have considered the c onnection between localization and transport in the low-density limit and the possible applications of the method to understanding of the ph ysical properties of some systems with low-dimensionality.