An Extended Network Model with a Packages Diffusion Process

Abstract

The dynamics of a packages diffusion process within a selforganized network is analytically studied by means of an extended $f$% -spin facilitated kinetic Ising model (Fredrickson-Andersen model) using a Fock-space representation for the master equation. To map the three component system (active, passive and packages cells) onto a lattice we apply two types of second quantized operators. The active cells correspond to mobile states whereas the passive cells correspond to immobile states of the Fredrickson-Andersen model. An inherent cooperativity is included assuming that the local dynamics and subsequently the local mobilities are restricted by the occupation of neighboring cells. Depending on a temperature-like parameter $h^{-1}$ (interconnectivity) the diffusive process of the packages (information) can be almost stopped, thus we get a well separation of the time regimes and a quasi-localization for the intermediate range at low temperatures.