Universal spreading of wavepackets in disordered nonlinear systems

TL;DR

This paper investigates how wavepackets spread in disordered nonlinear systems, revealing a universal subdiffusive behavior characterized by a specific spreading exponent due to weak chaos and resonance effects.

Contribution

It demonstrates that wavepacket spreading in such systems is universally subdiffusive with an exponent of 1/3, driven by weak chaos and resonance mechanisms, regardless of initial conditions.

Findings

Wavepackets exhibit subdiffusive spreading with an exponent of 1/3.

Spreading is due to weak chaos and resonant modes within the packet.

The process is universal across different disordered nonlinear systems.

Abstract

In the absence of nonlinearity all eigenmodes of a chain with disorder are spatially localized (Anderson localization). The width of the eigenvalue spectrum, and the average eigenvalue spacing inside the localization volume, set two frequency scales. An initially localized wavepacket spreads in the presence of nonlinearity. Nonlinearity introduces frequency shifts, which define three different evolution outcomes: i) localization as a transient, with subsequent subdiffusion; ii) the absence of the transient, and immediate subdiffusion; iii) selftrapping of a part of the packet, and subdiffusion of the remainder. The subdiffusive spreading is due to a finite number of packet modes being resonant. This number does not change on average, and depends only on the disorder strength. Spreading is due to corresponding weak chaos inside the packet, which slowly heats the cold exterior. The second moment of the packet is increasing as $t^{\alpha}$. We find $\alpha=1/3$.