Condensation in zero-range processes on inhomogeneous networks

We investigate the role of inhomogeneities in zero-range processes in condensation dynamics. We consider the dynamics of balls hopping between nodes of a network with one node of degree k₁ much higher than a typical degree k , and find that the condensation is triggered by the inhomogeneity and that it depends on the ratio k₁k . Although, on the average, the condensate takes an extensive number of balls, its occupation can oscillate in a wide range. We show that in systems with strong inhomogeneity, the typical melting time of the condensate grows exponentially with the number of balls.