Annihilation rate and scaling in a two-dimensional system of charged particles.

We study numerically the dynamic evolution of a two-dimensional system of charged particles which interact with a logarithmic potential, move with constant mobility, and annihilate on contact with an opposite charge. It is shown that in the diffusive regime, at high temperature where Brownian motion dominates, the number density decay is described by a power law with the exponent -0.55\ifmmode\pm\else\textpm\fi{}0.05, which is in agreement with theoretical result -0.5. In the deterministic regime, where motion is controlled by the interparticle forces, the exponent is -0.90\ifmmode\pm\else\textpm\fi{}0.05. A simple scaling hypothesis is suggested to explain this unusual exponent.