One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems

TL;DR

This paper introduces a one-parameter scaling law for stationary states in disordered nonlinear systems, providing a new framework to understand the interplay between Anderson localization and nonlinearity.

Contribution

It presents a novel scaling law for stationary solutions in disordered nonlinear lattices, combining numerical analysis and theoretical insights.

Findings

Normalized participation number obeys a one-parameter scaling law

The approach links Anderson localization with nonlinearity through scaling theory

Provides a new methodology for studying disordered nonlinear systems

Abstract

We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scaling law. Our approach opens a new way to investigate the interplay of Anderson localization and nonlinearity based on the powerful ideas of scaling theory.