Stationary scattering from a nonlinear network

TL;DR

This paper extends stationary scattering theory to nonlinear quantum graphs, revealing that cycles cause sharp resonances highly sensitive to nonlinearity, leading to multistability and hysteresis, with applications in optical networks.

Contribution

It introduces a framework for analyzing nonlinear scattering on complex networks, highlighting the impact of cycles on resonance behavior and nonlinearity effects.

Findings

Cycles induce sharp, nonlinear-sensitive resonances.

Resonances exhibit multistability and hysteresis.

Framework applicable to optical network light propagation.

Abstract

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multi-stability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.