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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2015

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

Résumé

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.
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hal-01064458 , version 1 (24-09-2014)
hal-01064458 , version 2 (23-11-2015)

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Martial Defoort, Vadim Puller, Olivier Bourgeois, Fabio Pistolesi, Eddy Collin. Scaling laws for the bifurcation-escape rate in a nanomechanical resonator. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (5), pp.050903(R). ⟨10.1103/PhysRevE.92.050903⟩. ⟨hal-01064458v2⟩
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