Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD

We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined - Reggeon Field Theory, Directed Percolation and Reversible Processes - only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.