Two Centuries of Diffusion

This talk will cover more than two century-old history of
Diffusion. What started from the French school of mathematical
physicists, primarily Fourier and Laplace, who had introduced us to
two distinct paradigms of diffusion -- physical and stochastic, the
topic still occupies our space with its various ramifications. It is a
subject that intertwines mathematics with observed phenomena,
illustrated by Brown's findings of random zig-zag motion of pollen
particles in a tube of water, kept at a fixed temperature .Thus,
almost a century after Fourier and Laplace talked about physical and
stochastic diffusion, Einstein unified the two disparate concepts
through his path-breaking work on Brownian motion.  Diffusion and
co-operative interactions is another area of contemporary interest in
the Chemistry and Physics of Materials and Biology. Thus,
reaction-diffusion equations are at the core of pattern formation,
morphogenesis and fractal colony growth of biological species.

In the second part of the talk, we move to the subatomic arena when
one asks what happens to an elementary particle such as an electron or
a proton that undergoes diffusive motion. Their dynamic behavior, in
interaction with their surroundings, leads to dissipative motion,
which invariably necessitates the investigation of diffusion in the
quantum domain. That study therefore directly impacts the contemporary
subjects of dissipative tunneling, Landau diamagnetism,
coherence-to-deceoherence transition, quantum information processes,
and so on.