Multimodal stationary states under Cauchy noise

A L\'evy noise is an efficient description of out-of-equilibrium systems. The presence of L\'evy flights results in a plenitude of noise-induced phenomena. Among others, L\'evy 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.