# Scaling laws for the bifurcation-escape rate in a nanomechanical resonator

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* Corresponding author 1 UBT - Ultra-basses températures NEEL - Institut Néel 2 LOMA - Laboratoire Ondes et Matière d-Aquitaine 3 NEEL - Institut Néel

Abstract : We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in cryogenic environment. By tuning in situ the non-linear coefficient $\gamma$ we could explore a wide range of the parameter space around the bifurcation point, where the metastable state becomes unstable. We measured in a relaxation process the distribution of the escape times. We have been able to verify its exponential distribution and extract the escape rate $\Gamma$. We investigated the scaling of $\Gamma$ with respect to the distance to the bifurcation point and $\gamma$, finding an unprecedented quantitative agreement with the theoretical description of the stochastic problem. Simple power scaling laws turn out to hold in a large region of the parameter-s space, as anticipated by recent theoretical predictions. These unique findings, implemented in a model dynamical system, are relevant to all systems experiencing under-damped saddle-node bifurcation.

Keywords : nonlinear phenomena nano-mechanics bifurcation

Autor: Martial Defoort - Vadim Puller - Olivier Bourgeois - Fabio Pistolesi - Eddy Collin -

Fuente: https://hal.archives-ouvertes.fr/

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