Spectral description of the dynamics of ultracold interacting bosons in disordered lattices

TL;DR

This paper analyzes the dynamics of ultracold interacting bosons in disordered lattices using spectral entropy and Lyapunov exponents, revealing how eigenstate properties influence different dynamical regimes.

Contribution

It introduces a spectral approach to characterize the dynamics of disordered bosonic systems, linking eigenstate shapes to chaotic and self-trapped behaviors.

Findings

Chaotic and self-trapped regimes follow log-normal laws.

Spectral quantities depend on initial states and explain long-term behavior.

Eigenstates exhibit exponential shapes influencing dynamics.

Abstract

We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short time dynamics, and shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system behaviour at longer times.