Noise-Induced Order in Extended Systems: A Tutorial

TL;DR

This tutorial reviews how external noise can induce order in spatially extended systems described by stochastic PDEs, highlighting key phenomena and current research status in noise-induced effects.

Contribution

It provides a comprehensive introduction and overview of noise-induced order phenomena in extended systems, emphasizing recent developments and foundational concepts.

Findings

External fluctuations can induce order in extended systems.

Noise effects include phase transitions and structure formation.

The paper summarizes key paradigmatic examples.

Abstract

External fluctuations have a wide variety of constructive effects on the dynamical behavior of spatially extended systems, as described by stochastic partial differential equations. A set of paradigmatic situations exhibiting such effects are briefly reviewed in this paper, in an attempt to provide a concise but thorough introduction to this active field of research, and at the same time an overview of its current status. This work is dedicated to Lutz Schimansky-Geier on the occassion of his 50th anniversary. Through the years, Prof. Schimansky-Geier has made important contributions to the field of spatiotemporal stochastic dynamics, including seminal investigations in the early 1990's on noise effects in front propagation, and studies of noise-induced phase transitions and noise-sustained structures in excitable media, among others.