Enhancement of stability of metastable states in the presence of Lévy noise

Abstract

The barrier-crossing event for superdiffusion characterized by symmetric Lévy 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 Lévy noise characterized by both an arbitrary index $\alpha$ and arbitrary noise intensity parameter. For the specific case of Lévy flights with an index $\alpha =1$ 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 Lévy noise.

arXiv comment18 pages, 3 figures

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• Inferring intermediate states by leveraging the many-body Arrhenius law
• Noise-Assisted Metastability: From Lévy Flights to Memristors, Quantum Escape, and Josephson-based Axion Searches