Proliferation of unstable states and their impact on stochastic out-of-equilibrium dynamics

TL;DR

This paper investigates how unstable states, especially ghost bifurcations, influence the stochastic out-of-equilibrium dynamics in networks of nonlinear parametric resonators, revealing their role in switching behavior.

Contribution

It uncovers the fundamental role of ghost bifurcations in noise-driven switching dynamics of nonlinear resonator networks, supported by experimental evidence.

Findings

Ghost bifurcations determine switching paths.

Unstable states influence noise-activated dynamics.

Experimental validation with coupled resonators.

Abstract

Networks of nonlinear parametric resonators are promising candidates as Ising machines for annealing and optimization. These many-body out-of-equilibrium systems host complex phase diagrams of coexisting stationary states. The plethora of states manifest via a series of bifurcations, including bifurcations that proliferate purely unstable solutions, which we term ``ghost bifurcations''. Here, we demonstrate that the latter take a fundamental role in the stochastic dynamics of the system in the presence of noise. Specifically, they determine the switching paths and the switching rates between stable solutions. We demonstrate experimentally the impact of ghost bifurcations on the noise-activated switching dynamics in a network of two coupled parametric resonators.