Spontaneous repulsion in the A +B →0 reaction on coupled networks

We study the transient dynamics of an A +B →0 process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions q of cross couplings, the concentration of A (or B ) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time t_x. By numerical and analytical arguments, we show that for symmetric and homogeneous structures t_x∝(<k>/q)log(<k>/q) where <k > is the mean degree of both networks. Being this behavior is in marked contrast with a purely diffusive process, where the mixing time would go simply like <k >/q , we identify the logarithmic slowing down in t_x to be the result of a spontaneous mechanism of repulsion between the reactants A and B due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.