Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

TL;DR

This paper presents an exact analytical model to study phase transitions in systems influenced by Le9vy stable noise, expanding understanding beyond numerical methods in fractional Fokker-Planck equations.

Contribution

It introduces an analytically solvable model for phase transitions driven by Le9vy noise, providing explicit solutions and stability analysis.

Findings

Exact solutions for fractional Fokker-Planck equations with Le9vy noise

Identification of phase transition conditions under Le9vy noise

Enhanced understanding of stability in nonlinear stochastic systems

Abstract

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of L\'evy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with L\'evy noise have attracted much attention and behaviors of systems with double-well potential subjected to L\'evy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an {\it analytically solvable model} to study the occurrence of phase transitions driven by L\'evy stable noise.