Diffusion and Brownian Motion Analogies in the Migration of Atoms, Animals, Men and Ideas

The macroscopic laws of diffusion were laid down for the case of liquids by Adolf Fick 150 years ago who realised the analogy of diffusion and heat conduction. 100 years ago Einstein and Smoluchowski put up the equation named after these scientists teaching us how to trace down the motion of a single diffusing particle and thus to understand long time unexplained Brownian motion as a fluctuation phenomenon. In the last fifty years these laws and their combination were boldly but successfully applied to the diffusion, migration, dispersion of single atoms, men, animals and ideas. We start by showing how the Einstein-Smoluchowski equation makes possible to induce diffusivity from microscopic information on details of the diffusion jump in solids. We then report on Brownian motion and diffusion of our fore-fathers in the Neolithicum following Cavalli-Sforza’s ideas and show how this diffusion must have been a mixture of demic diffusion, i.e. the diffusion of people, and the diffusion of technological ideas. Next we risk a glimpse to the immigration of early Americans. We point out the discrepancy a physicist faces in the conclusions of the Archaeologists. We finally discuss the ultra-fast dispersion of the horse-chestnut leaf miner throughout Europe following recent work of ecologists.