Temporal Diffusion
arXiv:cond-mat/0302420 · doi:10.1209/epl/i2003-00521-4
Abstract
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 \emph{propagation-dispersion equation} which is obtained as the continuous limit of the exact microscopic \emph{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 \emph{temporal diffusion}, which is a generic behavior encountered in an important class of systems.
7 pages including one figure