Electronic response in a one-dimensional nonlinear lattice.

Abstract

We study electronic response in a one-dimensional nonlinear lattice in terms of a transmission problem where the nonlinear Schr\"odinger equation of the tight-binding form is considered to describe the motion of the electrons. We introduce an area-preserving nonlinear mapping for the transmission problem. We then analyze this mapping in the context of nonlinear dynamical theory, and discuss the results in terms of physical quantities describing the transmission process. We show a ``phase diagram'' in terms of the electronic energy and nonlinear coupling constant for the solutions which contribute to the transmission. We also calculate the transmission coefficients as functions of the nonlinear coupling constant. Our results demonstrate how interesting properties, such as multistability and noise, occur in the electronic response of our problem. Several physical models involving electronic or optical processes are considered as systems that might be relevant to our study.