Nonlinear Supratransmission

TL;DR

This paper demonstrates nonlinear supratransmission in mechanical and Josephson systems, showing energy transmission in forbidden band gaps due to nonlinear instabilities, with experimental and theoretical insights.

Contribution

It provides experimental realization and detailed analysis of nonlinear supratransmission in mechanical and Josephson systems, extending understanding beyond integrable models.

Findings

Nonlinear supratransmission occurs at predictable thresholds.

Experimental realization with a mechanical pendula chain.

Sustained in Josephson transmission lines despite damping.

Abstract

A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for the nonlinear chain of coupled pendula [Phys Rev Lett 89 (2002) 134102]. This process of nonlinear supratransmission, occurring at a threshold exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendula coupled by a coil spring. It is then analyzed in more detail by first going to different (non-integrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (one dimensional array of short Josephson junctions coupled through super-conducting wires), is shown to sustain also nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness and discreteness. Finally the mechanism at the origin of nonlinear supratransmission is a nonlinear instability, and it is briefly discussed here.