Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices

TL;DR

This paper investigates the scaling behavior of weak chaos in nonlinear disordered lattices modeled by the Discrete Nonlinear Schrödinger Equation, revealing how system parameters influence regularity and chaos.

Contribution

It introduces a scaling function for the probability of regularity in the system, enabling analysis of asymptotic properties beyond computational limits.

Findings

Probability of regularity follows a scaling law

Asymptotic properties can be predicted using the scaling function

Nonlinearity and disorder strength significantly affect system dynamics

Abstract

The Discrete Nonlinear Schroedinger Equation with a random potential in one dimension is studied as a dynamical system. It is characterized by the length, the strength of the random potential and by the field density that determines the effect of nonlinearity. The probability of the system to be regular is established numerically and found to be a scaling function. This property is used to calculate the asymptotic properties of the system in regimes beyond our computational power.