Wed Nov 30 2005

Brownian motion was discovered by a botanist named Brown, when he looked at water under a microscope, and observed pollen grains "jiggling" about in it. Einstein eventually explained it as due to the random collisions the pollen grain experienced from the water molecules. We compare the pollen grain to a drunk person walking home, and calculate how far the pollen grain can get by this type of diffusion. We also introduce the fluctuation-dissipation theorem, a far-reaching principle in advanced statistical mechanics that says that the microscopic thermal fluctuations in a system are the same microscopic processes that are responsible for things like drag, viscosity, and electrical resistance. (Why is that so cool? Because it means you can predict nonequilibrium properties -- those in the presence of an applied field like voltage -- to equilibrium properties like thermal fluctuations.) We also derive Fick's law of diffusion -- particles diffuse away from high concentrations. Go figur...