Destruction of Anderson localization by a weak nonlinearity

TL;DR

This paper demonstrates through numerical simulations that weak nonlinearity can destroy Anderson localization in a disordered 1D lattice, leading to subdiffusive wave spreading with a specific growth exponent.

Contribution

It reveals the critical nonlinearity strength needed to break Anderson localization and characterizes the resulting subdiffusive spreading behavior.

Findings

Localization persists at low nonlinearities

Above critical nonlinearity, wave spreads subdiffusively

Growth exponent of spreading is between 0.3 and 0.4

Abstract

We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schr\"odinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time $ \propto t^\alpha$, with the exponent $\alpha$ being in the range $0.3 - 0.4$. For small nonlinearities the distribution remains localized in a way similar to the linear case.