Transmission thresholds in time-periodically driven nonlinear disordered systems

TL;DR

This paper investigates how energy propagates in disordered nonlinear chains under periodic driving, identifying different regimes of localization, weak chaos, and spreading depending on the driving amplitude and frequency.

Contribution

It introduces a detailed analysis of transmission thresholds in driven nonlinear disordered systems, combining analytical bifurcation analysis with numerical methods.

Findings

Thresholds depend on bifurcations in the system

Three regimes of energy propagation identified

Threshold remains nonzero for infinite chains

Abstract

We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) Below threshold, localized quasiperiodic oscillations and no spreading; 2) Three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times, and finally strong diffusion; 3) Immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning-points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.