Role of long jumps in L\'evy noise induced multimodality

Abstract

L\'evy noise is a paradigmatic noise used to describe out-of-equilibrium systems. Typically, properties of L\'evy noise driven systems are very different from their Gaussian white noise driven counterparts. In particular, under action of L\'evy noise, stationary states in single-well, super-harmonic, potentials are no longer unimodal. Typically, they are bimodal however for fine-tuned potentials the number of modes can be further increased. The multimodality arises as a consequence of the competition between long displacements induced by the non-equilibrium stochastic driving and action of the deterministic force. Here, we explore robustness of bimodality in the quartic potential under action of the L\'evy noise. We explore various scenarios of bounding long jumps and assess their ability to weaken and destroy multimodality. In general, we demonstrate that despite its robustness it is possible to destroy the bimodality, however it requires drastic reduction in the length of noise-induced jumps.