A self-consistent theory of localization in nonlinear random media

TL;DR

This paper extends the self-consistent theory of localization to nonlinear media, showing that weak nonlinearity destroys Anderson localization and induces subdiffusion, replacing the transition with a subdiffusion-diffusion transition in 3D.

Contribution

It introduces a generalized self-consistent theory that incorporates weak quadratic nonlinearity, revealing its impact on localization and transport phenomena.

Findings

Nonlinearity destroys Anderson localization in weakly nonlinear media.

Wave packets exhibit algebraic subdiffusion instead of localization.

In 3D, a subdiffusion-diffusion transition replaces the Anderson transition.

Abstract

The self-consistent theory of localization is generalized to account for a weak quadratic nonlinear potential in the wave equation. For spreading wave packets, the theory predicts the destruction of Anderson localization by the nonlinearity and its replacement by algebraic subdiffusion, while classical diffusion remains unaffected. In 3D, this leads to the emergence of a subdiffusion-diffusion transition in place of the Anderson transition. The accuracy and the limitations of the theory are discussed.