Sub-Power Law Decay of the Wave Packet Maximum in Disordered Anharmonic Chains

TL;DR

This paper demonstrates that in disordered nonlinear chains, the maximum of an initially localized wave packet decays slower than any power law over time, revealing a novel slow decay behavior in such systems.

Contribution

It introduces the finding that wave packet peaks decay sub-power-law in disordered nonlinear chains, extending understanding of wave dynamics in these complex systems.

Findings

Wave packet peaks decay slower than any power law.

Results apply to long-time, almost sure scenarios.

Valid for arbitrary finite energy values.

Abstract

We show that the peak of an initially localized wave packet in one-dimensional nonlinear disordered chains decays more slowly than any power law of time. The systems under investigation are Klein-Gordon and nonlinear disordered Schr\"odinger-type chains, characterized by a harmonic onsite disordered potential and quartic nearest-neighbor coupling. Our results apply in the long-time limit, hold almost surely, and are valid for arbitrary finite energy values.