Enhancement of stability of metastable states in the presence of L\'evy noise
Abstract
The barrier-crossing event for superdiffusion characterized by symmetric L\'evy flights is analyzed. Starting from the fractional Fokker-Planck equation, we derive an integro-differential equation along with the necessary conditions to calculate the mean residence time of a particle within a fixed interval. We consider an arbitrary smooth potential profile, particularly metastable, with a sink and L\'evy noise characterized by both an arbitrary index α and arbitrary noise intensity parameter. For the specific case of L\'evy flights with an index α = 1 and a cubic metastable potential, a closed expression for the mean residence time is obtained in quadratures. The analytical results reveal an enhancement of the mean residence time in the metastable state due to the influence of L\'evy noise.
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