Condensation in a zero range process on weighted scale-free networks.

We study the condensation phenomenon in a zero range process on weighted scale-free networks in order to show how the weighted transport influences the particle condensation. Instead of the approach of grand canonical ensemble which is generally used in a zero range process, we introduce an alternate approach of the mean-field equations to study the dynamics of particle transport. We find that the condensation on the scale-free network is easier to occur in the case of weighted transport than in the case of weight-free networks. In the weighted transport, especially, a dynamical condensation is even possible for the case of no interaction among particles, which is impossible in the case of weight-free networks.