Mass Transport Models on Networks

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The study of mass transport processes in one-and two dimensional systems led to considerable progress in the understanding of statistical systems out-of-equilibrium, for which guiding principles and classification schemes are missing in general. Usually these studies focus on simple regular topologies. On the other hand, a variety of out-of-equilibrium processes is going on in natural systems, which are nowadays summarized under complex networks. The analysis of dynamical processes on complex networks is just in their infancy. An important class of processes is mass transport ( mass in a generic sense of flow of particles, energy, information or traffic) for which we shall implement the ubiquitous noise, inherent in any transport, via a stochastic description. We shall focus on generalizations of the zero-range process on non-trivial topologies, which may serve as building blocks for larger networks in the spirit of the renormalization group, but remain analytically tractable. For the field of network dynamics this should provide an analytic understanding as well as steps towards an embedding into a larger context and a classification of stationary states observed in network simulations. From the perspective of statistical physics out-of-equilibrium, our project aims at generalizations towards more realistic geometries, real processes such as protein traffic inside cells, and more realistic (e.g. open) boundary conditions, non-zero range processes with short- and long-range interactions and feedbacks, extensions of fluctuation theorems and analysis of transients in the approach of stationary states. The expertise of our two groups in mass transport and numerical simulations (W. Janke) and network dynamics and analytical calculations (H. Meyer-Ortmanns) will supplement each other and lead to a productive collaboration when it is combined.