Reaction-controlled diffusion

The dynamics of a coupled two-component nonequilibrium system is examined b y means of continuum field theory representing the corresponding master equ ation. Particles of species A may perform hopping processes only when parti cles of different type B are present in their environment. Species B is sub ject to diffusion-limited reactions. If the density of B particles attains a finite asymptotic value (active state), the A species displays normal dif fusion. On the other hand, if the B density decays algebraically proportion al tot(-alpha) at long times (inactive state), the effective attractive A-B interaction is weakened. The combination of B decay and activated A hoppin g processes gives rise to anomalous diffusion, with mean-square displacemen t ((x) over right arrow (A)(t)(2)) proportional to t(1-alpha) for alpha <1. Such algebraic subdiffusive behavior ensues for nth-order B annihilation r eactions (nB-->O) with n greater than or equal to 3, and n = 2 for d<2. The mean-square displacement of the A particles grows only logarithmically wit h time in the case of B pair annihilation (n = 2) and d<greater than or equ al to>2 dimensions. For radioactive B decay (n = 1), the A particles remain localized. If the A particles may hop spontaneously as well, or if additio nal random forces are present, the A-B couplings becomes irrelevant, and co nventional diffusion is recovered in the long-time limit.