Logarithmic expansion of many-body wave packets in random potentials

TL;DR

This paper investigates the quantum dynamics of many-body wave packets in disordered potentials, revealing a universal logarithmic expansion regime that bridges initial diffusion and eventual saturation, influenced by particle number and localization length.

Contribution

It introduces a universal logarithmic expansion regime in many-body wave packets, connecting mean-field diffusion to saturation, controlled by particle number and localization length.

Findings

Observation of saturation of wave packet volume to N times the localization length

Identification of a universal logarithmic expansion regime

Exponential growth of the regime's temporal window with localization length

Abstract

Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $\xi$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by (i) using the ultrafast unitary Floquet dynamics of discrete-time quantum walks, (ii) an interaction strength ramping to speed up the subdiffusion, and (iii) an action discretization of the nonlinear terms. We observe the saturation of the cloud expansion of $N$ particles to a volume $\sim N\xi$. We predict and observe a universal intermediate logarithmic expansion regime which connects the mean-field diffusion with the final saturation regime and is entirely controlled by particle number $N$. The temporal window of that regime grows exponentially with the localization length $\xi$.