Absence of Wavepacket Diffusion in Disordered Nonlinear Systems

TL;DR

This paper demonstrates that in disordered nonlinear systems, wavepackets do not undergo diffusion but instead settle into nondecaying, quasiperiodic states, challenging previous assumptions about energy spreading.

Contribution

The study analytically proves the absence of wavepacket diffusion in certain nonlinear disordered systems and characterizes their long-term quasiperiodic behavior.

Findings

Participation number remains bounded over time.

Wavepackets evolve into nondecaying, interacting normal modes.

Fourier spectrum indicates quasiperiodic dynamics.

Abstract

We study the spreading of an initially localized wavepacket in two nonlinear chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverge as a function of time. We find that the participation number of a wavepacket does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times the dynamical state consists of a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wavepacket, a limit profile for the norm/energy distribution with infinite second moment should exist in all cases which rules out the possibility of slow energy diffusion (subdiffusion). This limit profile could be a quasiperiodic solution (KAM torus).