Similarity transformation in one-dimensional reaction-diffusion systems: the voting model as an example

The exact solution for a system with two-particle annihilation and decoagul ation has been studied. The spectrum of the Hamiltonian of the system is fo und. It is shown that the steady state is twofold degenerate. The average n umber density at each site [n(i)(t)] and the equal-time two-point functions [n(i)(t)n(j)(t)] are calculated. Any equal-time correlation functions at l arge times, [n(i)(infinity )n(j)(infinity)...], are also calculated. The re laxation behaviour of the system toward its final state is investigated and it is shown that generally it is exponential, as expected. For the special symmetric case, the relaxation behaviour of the system is a power law. For the asymmetric case, it is shown that the profile of deviation from the fi nal values is an exponential function of the position.