Classical and Quantum Models of Diffusion

Abstract

The objective of the paper is twofold: first, to review the classical diffusion models and show the approximations at the origin of the parabolic character of the classical equations; second, to demonstrate a connection between the quantum and classical models of diffusion. As diffusion is inherently related to the motion of constituents, the consistent models are framed within the dynamics of mixtures. The derivation of diffusion equations is then determined based on the related, pertinent approximations.