Dinâmica eletrônica em cadeias unidimensionais não-lineares discretas, nos limites adiabático e não-adiabático

Abstract

Fundamental problem on Condensed Matter Physics is the study of electronic transport phenomena in solids. In this context, a particularly important nonlinear phenomenon is the interaction of the lattice vibrational modes on electrons in a solid, usually called electron-phonon interacion. This sort of problem has been studied by means of nonlinear discrete quantum evolution of the wave-packet associated with the quasiparticle. An alternative to this approach, usually found in the literature, is the use of discrete nonlinear Schrödinger equation, which is based on the assumption that lattice vibrations reach their equilibrium in a very short time relative to the evolution of the quasiparticle (adiabatic limit). Although this approach has obtained very successful results on the study of quasiparticles dynamics in solids, new effects can arise when the adiabatic hypothesis is left, i.e., by considering a finite time for the relaxation of lattice vibrations in the equations. In this work we analyse the electronic dynamics in na unidimensional discrete chain, using periodic boundary conditions, to investigate the influence of a nonlinearity (modulated by the parameter x) which effectivelly represents the electron-phonon interaction, on the adiabatic and non-adiabatic limits for this nonlinearity. We observed in both limits that, above a critical value of nonlinearity, the electron-phonon interaction induces a metal-insulator transition on the system by means of self-trapping phenomenon. Furthermore, it was observed a rich dynamical behaviour for the electron according to values of nonlinearity; in more details, three dynamical regimes in the adiabatic case and five dynamical regimes in the non-adiabatic case.