DISORDER IN THE DISCRETE NONLINEAR SCHRÖDINGER EQUATION

Abstract

We study the interplay of disorder and nonlinearity in condensed matter systems modeled by the paradigmatic discrete nonlinear Schrödinger equation and focus on selftrapping and transport properties. We start by analyzing the two most simple nonlinear disordered systems, viz. a nondegenerate nonlinear dimer and a perturbed degenerate dimer. We then consider the case of few nonlinear impurities embedded in a linear host and treat the stationary problem analytically. We conclude by examining the case of a one-dimensional nonlinear random binary alloy where we find absence of quasiparticle localization, except for large nonlinearity parameter values. The transmission of plane’ waves across a disordered nonlinear segment of this type shows a power-law decay as a function of the segment size.