Time evolution of models described by one-dimensional discrete nonlinear Schr\"odinger equation

TL;DR

This paper investigates the time evolution of one-dimensional discrete nonlinear Schrödinger models, revealing phenomena like cluster-trapping, self-trapping, soliton-like waves, and ballistic propagation, with implications for nonlinear impurity effects.

Contribution

It provides a detailed analysis of nonlinear dynamics in discrete Schrödinger models, including transitions and wave behaviors, under various initial conditions and system configurations.

Findings

Identification of cluster-trapping and self-trapping transitions.

Observation of soliton-like wave propagation in large clusters.

Ballistic propagation in random nonlinear systems.

Abstract

The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. First, various sizes of nonlinear cluster embedded in an infinite linear chain are considered. The initial excitation is applied either at the end-site or at the middle-site of the cluster. In both the cases we obtain two kinds of transition: (i) a cluster-trapping transition and (ii) a self-trapping transition. The dynamics of the quasiparticle with the end-site initial excitation are found to exhibit, (i) a sharp self-trapping transition, (ii) an amplitude-transition in the site-probabilities and (iii) propagating soliton-like waves in large clusters. Ballistic propagation is observed in random nonlinear systems. The effect of nonlinear impurities on the superdiffusive behavior of random-dimer model is also studied.