Condensation in the Zero Range Process: Stationary and Dynamical Properties

By Stefan Grosskinsky, Gunter M. Schütz, Herbert Spohn. 2003

207 citations recorded by the source corpus.

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.

Subfields: Condensed Matter Physics, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/8b3ce6c39ba167246c1129ef7d0f309a1e8898a4

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In Condensed Matter Physics

In Mathematical Physics

In Molecular Biology

Citations in the corpus

Tunneling and Metastability of Continuous Time Markov Chains (2009, unknown): “This family, known as the condensed zero-range processes, have been introduced in the physics literature [8, 13, 9] to model the Bose-Einstein condensation phenomena.”
Metastability of reversible condensed zero range processes on a finite set (2009, methodology): “The equivalence of ensembles has been proved by Großkinsky, Schütz and Spohn [8].”