The Importance of Being Discrete - Autocatalysis of Quantized Objects
   Nadav M. Shnerb
Dept. of Physics, College of Judea and Samaria
44839 Ariel, Israel 
 nadav@ycariel.yosh.ac.il

Evolution of a system of diffusing, mortal reactants is analyzed in the presence of randomly moving catalyzers. In particular, the regime where the mean-field, continuum description of the problem predicts extinction of the reactants is explored. It is shown that the discrete nature of the agents allows for an active phase, where reactants proliferate as their spatial configuration adapts to the fluctuations of the catalyzer density. The system is studied  by employing field theoretical techniques,
numerical simulations and strong coupling analysis. For d<2, the  system always flows towards its active phase, while for d>2, a kinetic phase transition is predicted. The applicability of this model as a prototype for a host of phenomena which exhibit self organization is discussed.

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