[048] Temporal diffusion

J. P. Boon, P. Grosfils, and J. F. Lutsko, "Temporal diffusion", EuroPhys. Lett., 63, 186 (2003) http://jimlutsko.github.io/files/J._P._Boon_2003_EPL_63_186


We consider the general problem of the first-passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a propagation-dispersion equation which is obtained as the large-distance (hydrodynamic) limit of the exact microscopic first-visit equation. The propagation-dispersion equation should be contrasted with the advection-diffusion equation as the roles of space and time are reversed, hence the name temporal diffusion, which is a generic behavior encountered in an important class of systems.