Regensburg 2016 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 26: Networks: From Topology to Dynamics (joint session DY / SOE / BP)

SOE 26.3: Talk

Thursday, March 10, 2016, 16:00–16:15, H47

The totally asymmetric inclusion process (TASIP): how network topology determines condensation and transport properties — •Johannes Knebel, Markus F. Weber, Philipp Geiger, and Erwin Frey — Ludwigs-Maximilians-Universität, München, Deutschland

Transport phenomena are often modeled by the hopping of particles on regular lattices or networks. Such models describe, for example, the exclusive movement of molecular motors along microtubules: no two motors may occupy the same site. In our work, we study inclusion processes that are the bosonic analogues of the fermionic exclusion processes. In inclusion processes, many particles may occupy a single site and hopping rates depend linearly on the occupation of departure and arrival sites. Particles thus attract other particles to their own site. Condensation occurs when particles collectively cluster in one or in multiple sites, whereas the other sites become depleted.

We showed that inclusion processes on a network describe both the selection of strategies in evolutionary zero-sum games and the condensation of non-interacting bosons into multiple quantum states in driven-dissipative systems. The condensation is captured by the antisymmetric Lotka-Volterra equation (ALVE), which constitutes a nonlinearly coupled dynamical system. We derived an algebraic method to analyze the ALVE and to determine the condensates. Our approach allows for the design of networks that result in condensates with oscillating occupations, and yields insight into the interplay between network topology and transport properties.