100 years of Einstein's theory of Brownian motion: from pollen grains to protein trains

Abstract

Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms. In the last 100 years discoveries of many facets of the ubiquitous Brownian motion has revolutionized our fundamental understanding of the role of {\it thermal fluctuations} in the exotic structures and complex dynamics exhibited by soft matter like, for example, colloids, gels, etc. The domain of Brownian motion transcends the traditional disciplinary boundaries of physics and has become an area of multi-disciplinary research. Brownian motion finds applications also in earth and environmental sciences as well as life sciences. Nature exploits Brownian motion for running many dynamical processes that are crucial for sustaining life. In the first one-third of this article I present a brief historical survey of the initial period, including works of Brown and Einstein. In the next one-third I introduce the main concepts and the essential theoretical techniques used for studying translational as well as rotational Brownian motions and the effects of time-independent potentials. In the last one-third of this article I discuss some contemporary problems on Brownian motion in time-dependent potentials, namely, {\it stochastic resonance} and {\it Brownian ratchet}, two of the hottest topics in this area of interdisciplinary research.