Overshooting Currents and Condensation Transitions in the Zero-Range process

Andrew Angel

University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, U.K.

The zero-range process is a simple hopping particle model which has an exactly soluble steady state and can exhibit condensation transitions in the thermodynamic limit. In cases that have such transitions the current versus particle density diagram is monotonically increasing below the critical density and constant above it. In large but finite systems condensation-like crossover phenomena can be observed, accompanied with an 'overshoot' in the current. Here the current increases beyond the constant value expected from the thermodynamic limit before dropping back down towards it at higher densities. This phenomenon and its analysis in the canonical and grand canonical ensembles will be discussed. Related phenomena and applications of the zero-range process will also be touched upon.