Sensitivity to the initial state of interacting ultracold bosons in disordered lattices

TL;DR

This paper investigates how the initial state influences the dynamics of interacting ultracold bosons in disordered lattices, introducing a scaling law that characterizes localization regardless of initial conditions.

Contribution

It presents an analytical model that defines a global localization measure obeying a scaling law, advancing understanding of initial state sensitivity in disordered nonlinear systems.

Findings

The localization measure follows a specific scaling law.

The model characterizes dynamics independently of initial state.

Provides insights into the interplay of disorder and nonlinearity.

Abstract

We study the dynamics of a nonlinear one-dimensional disordered system obtained by coupling the Anderson model with the Gross-Pitaevskii equation. An analytical model provides us with a single quantity globally characterizing the localization of the system. This quantity obeys a scaling law with respect to the width of the initial state, which can be used to characterize the dynamics independently of the initial state.