Linear and nonlinear Anderson localization in a curved potential

TL;DR

This paper explores how disorder, nonlinearity, and curvature influence wave localization, revealing that curvature enhances localization effects through numerical simulations and a unified analytical theory.

Contribution

It introduces a self-consistent analytical framework linking randomness, nonlinearity, and geometry with a single scaling parameter, demonstrating curvature's role in localization enhancement.

Findings

Curvature increases wave localization in disordered nonlinear systems.

A unified scaling parameter captures the interplay of disorder, nonlinearity, and geometry.

Numerical simulations confirm the analytical predictions.

Abstract

We investigate disorder induced localization in the presence of nonlinearity and curvature. We numerically analyze the time-resolved three-dimensional expansion of a wave-packet in a bended cigar shaped potential with a focusing Kerr-like interaction term and Gaussian disorder. We report on a self-consistent analytical theory in which randomness, nonlinearity and geometry are determined by a single scaling parameter, and show that curvature enhances localization.