A self-consistent theory of localization in nonlinear random media
Disordered Systems and Neural Networks
2017-07-06 v2
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.
Cite
@article{arxiv.1607.08519,
title = {A self-consistent theory of localization in nonlinear random media},
author = {Nicolas Cherroret},
journal= {arXiv preprint arXiv:1607.08519},
year = {2017}
}
Comments
Revised version