Phase transitions driven by Lévy stable noise: Exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Department of Applied Physics, Faculty of Science, Tokyo Institute of Technology - 2-12-1 Ohokayama, Meguro-ku, Tokyo, Japan

Corresponding author: aichiki@mikan.ap.titech.ac.jp

Received: 1 May 2009
Accepted: 24 July 2009

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 Lévy 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 Lévy noise have attracted much attention and behaviors of systems with double-well potential subjected to Lévy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an analytically solvable model to study the occurrence of phase transitions driven by Lévy stable noise.