Noise Induced Phenomena: a Sampler

摘要

Fluctuations or noise have played a changing role in the history of science. Historically, we can identify three views of noise. In the first, up to the end of the 19th century, noise was considered a nuisance to be avoided or eliminated. This is still the implication of the definition of the word noise in any standard dictionary. A second stage dates from the beginning of the 20th century, when it became clear from the study of fluctuations via Onsager relations and fluctuation-dissipation relations that one can obtain useful information about a physical system from its fluctuations. The third stage started about three decades ago, and is marked by the realization that noise can actually play a central role in inducing new phenomena. Examples where noise leads to organized behavior include stochastic resonance, noise-induced phase transitions, noise-induced pattern formation, and noise-induced transport. In this minicourse we sample some such noise-induced phenomena. While many of these fluctuation-induced phenomena involve temporal fluctuations, spatial fluctuations (disorder) can also play a similar organizing role. We briefly illustrate this scenario as well.