Visualizing Anderson Localization in 3d using Monte Carlo method

TL;DR

This paper investigates Anderson localization effects on a 3D Bose-Einstein condensate in disordered potentials using Monte Carlo simulations, revealing how interactions influence localization properties.

Contribution

It introduces a Monte Carlo approach to study localization in 3D Bose-Einstein condensates, analyzing the interplay of disorder and interactions with detailed numerical results.

Findings

Localization length varies with disorder strength

Wave functions become more delocalized with increased interaction

Identifies mobility edge and density profiles in the system

Abstract

We study the effect of Anderson localization on a Bose-Einstein condesate in 3d in a disordered potential by Feynman-Kac path integral technique. Simulations are performed in continuous space using canonical ensemble. Owing to the high degree of control over the system parameters we also study the interplay of disorder and interaction in the system. We numerically compute the localization length, mobility edge and the density profile of the condensate. We observe that as the interaction strength increases, the wave functions become more and more delocalized.