# Multimodal stationary states under Cauchy noise

## TL;DR

This paper investigates how Le9vy noise influences stationary states in double-well potentials, revealing conditions for bimodality and its impact on noise-induced escape phenomena.

## Contribution

It demonstrates that high potential barriers can induce bimodal stationary states in each well under Le9vy noise, and analyzes how barrier height affects multimodality.

## Key findings

- High barriers lead to bimodal stationary states.
- Decreasing barrier height reduces multimodality.
- Multimodality influences noise-induced escape dynamics.

## Abstract

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.