Multimodal stationary states under Cauchy noise

Abstract

A Lévy noise is an efficient description of out-of-equilibrium systems. The presence of Lévy flights results in a plenitude of noise-induced phenomena. Among others, Lévy flights can produce stationary states with more than one modal value in single-well potentials. Here, we explore stationary states in special double-well potentials demonstrating that a sufficiently high potential barrier separating potential wells can produce bimodal stationary states in each potential well. Furthermore, we explore how the decrease in the barrier height affects the multimodality of stationary states. Finally, we explore a role of the multimodality of stationary states on the noise induced escape over the static potential barrier.

arXiv comment10 pages, 11 figures

References in corpus (15)

• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Levy Flight Superdiffusion: An Introduction
• Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• Anomalous jumping in a double-well potential
• Levy Anomalous Diffusion and Fractional Fokker--Planck Equation
• Lévy flights in a steep potential well
• Lévy flights of photons in hot atomic vapours
• From the area under the Bessel excursion to anomalous diffusion of cold atoms
• Levy Flights in External Force Fields: From Models to Equations
• Escape driven by $\alpha$-stable white noises
• Steady-State Lévy Flights in a Confined Domain
• Stationary states in single-well potentials under symmetric Levy noises
• Levy flights in confining potentials
• Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise

Cited by in corpus (5)

• Lévy noise-driven escape from arctan potential wells
• Peculiarities of escape kinetics in the presence of athermal noises
• A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics
• Shortcuts To Adiabaticity for Lévy processes in harmonic traps
• Role of long jumps in Lévy noise induced multimodality