Anderson localization as position-dependent diffusion in disordered waveguides

TL;DR

This paper demonstrates that Anderson localization in disordered waveguides can be accurately described by a position-dependent diffusion model, validated through theoretical and numerical approaches.

Contribution

It establishes the quantitative agreement between a self-consistent theory with position-dependent diffusion and supersymmetry and ab-initio simulations for disordered waveguides.

Findings

Agreement between theory and simulations up to 1/g_0^2 terms

Validation of position-dependent diffusion as a model for localization

Effective even with absorption in open media

Abstract

We show that the recently developed self-consistent theory of Anderson localization with a position-dependent diffusion coefficient is in quantitative agreement with the supersymmetry approach up to terms of the order of $1/g_0^2$ (with $g_0$ the dimensionless conductance in the absence of interference effects) and with large-scale {\it ab-initio} simulations of the classical wave transport in disordered waveguides, at least for $g_0 \gtrsim 0.5$. In the latter case, agreement is found even in the presence of absorption. Our numerical results confirm that in open disordered media, the onset of Anderson localization can be viewed as position-dependent diffusion.