Diffusion is the process behind Brownian motion. It was described by Albert Einstein in one of his annus mirabilis (1905) papers. The diffusion equation is that describes the process is
where is the (self-)diffusion coefficient. For initial conditions for a Dirac delta function at the origin, and boundary conditions that force the vanishing of and its gradient at large distances, the solution factorizes as , with a spreading Gaussian for each of the Cartesian components:
For a homogeneous system,
where is the center of mass velovity of molecule .