Resetting induced multimodality

TL;DR

This paper investigates how stochastic resetting combined with Lévy noise influences the number and nature of stationary states in out-of-equilibrium systems, revealing phase transitions in multimodality.

Contribution

It demonstrates that stochastic resetting can induce phase transitions in the multimodality of stationary states under Lévy noise in super-harmonic potentials.

Findings

Resetting can increase the number of stationary state modes.

High resetting rates suppress multimodality.

Resetting enables stationary states in sub-harmonic potentials.

Abstract

Properties of stochastic systems are defined by the noise type and deterministic forces acting on the system. In out-of-equilibrium setups, e.g., for motions under action of L\'evy noises, the existence of the stationary state is not only determined by the potential but also by the noise. Potential wells need to be steeper than parabolic in order to assure existence of stationary states. The existence of stationary states, in sub-harmonic potential wells, can be restored by stochastic resetting, which is the protocol of starting over at random times. Herein we demonstrate that the combined action of L\'evy noise and Poissonian stochastic resetting can result in the phase transition between non-equilibrium stationary states of various multimodality in the overdamped system in super-harmonic potentials. Fine-tuned resetting rates can increase the modality of stationary states, while for high resetting rates the multimodality is destroyed as the stochastic resetting limits the spread of particles.