Volume 87, Number 3, August 2009
Article Number 30004
Number of page(s) 5
Section General
Published online 27 August 2009
EPL, 87 (2009) 30004
DOI: 10.1209/0295-5075/87/30004

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

A. Ichiki and M. Shiino

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

received 1 May 2009; accepted in final form 24 July 2009; published August 2009
published online 27 August 2009

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.

05.40.Fb - Random walks and Levy flights.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
02.50.Ey - Stochastic processes.

© EPLA 2009