# Arbitrarily Weak Nonlinearity Can Destroy the Anderson Localization

## TL;DR

This paper demonstrates that even arbitrarily weak nonlinear interactions can destroy Anderson localization, leading to faster thermalization due to wave resonance effects, challenging previous assumptions about localization robustness.

## Contribution

It provides a theoretical analysis showing that weak nonlinearity destroys Anderson localization and accelerates thermalization through wave resonance mechanisms.

## Key findings

- Equipartition time scales as inverse square of nonlinearity strength.
- Weak nonlinearity cannot preserve Anderson localized modes.
- Disorder can enhance thermalization speed via three-wave resonance.

## Abstract

Whether the Anderson localization can survive from the weak enough nonlinear interaction is still an open question. In this Letter, we study the effect of nonlinear interaction on disordered chain based on the wave turbulence theory. It is found that the equipartition time $T_{eq}$ is inversely proportional to the square of the nonlinearity strength $\lambda$, i.e., $T_{eq}\propto\lambda^{-2}$, in thermodynamic limit. This result has two fundamentally important consequences. First, the Anderson localized modes can not survive from arbitrarily weak nonlinearity. Secondly, contrary to popular belief, disorder can lead to a more fast thermalization in the weak nonlinear region, which is due to the emergence of three-wave resonance.