Lattice gases with a point source
Abstract
We study diffusive lattice gases with local injection of particles, namely we assume that whenever the origin becomes empty, a new particle is immediately injected into the origin. We consider two lattice gases: a symmetric simple exclusion process and random walkers. The interplay between the injection events and the positions of the particles already present implies an effective collective interaction even for the ostensibly noninteracting random walkers. We determine the average total number of particles entering into the initially empty system. We also compute the average total number of distinct sites visited by all particles, and discuss the shape of the visited domain and the statistics of visits.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 September 2014
 DOI:
 10.1088/17425468/2014/09/P09003
 arXiv:
 arXiv:1407.0458
 Bibcode:
 2014JSMTE..09..003K
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 J. Stat. Mech. (2014) P09003