Anderson localization of excitations in disordered Gross-Pitaevskii lattices

TL;DR

This paper investigates how disorder affects excitations in a one-dimensional Gross-Pitaevskii lattice, revealing localization phenomena and the impact of interactions on excitation delocalization and localization length divergence.

Contribution

It provides analytical and numerical analysis of localization properties of excitations in disordered Gross-Pitaevskii lattices, including derivation of effective equations for strong interactions and generalization to higher dimensions.

Findings

Weak excitations delocalize at long wavelengths.

Strong interactions cause divergence of localization length at finite energy.

Effective field equations for excitations are derived and extended to higher dimensions.

Abstract

We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the weak and strong interaction regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov-de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For strong interactions, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective strong interaction field equations for the excitations and generalize to higher dimensions.