Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems
FRONTIERS IN PHYSICS(2019)
Abstract
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately.
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Key words
anomalous diffusion,fluctuation-dissipation theorem,generalized Langevin equation,Khinchin theorem,correlation functions,Fokker-Planck equation,growth processes,ergodicity breaking
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