Fractional exponential decay in the capture of ligands by randomly distributed traps

In many biophysical and biochemical experiments one observes the decay of some ligand population due to their capture by an appropriate system of traps. These experiments are usually interpreted under the assumption that the total number of free ligands decays as N(t) ≅ N0 exp(-tτ) for long times. It is pointed out that this result only holds when the traps are regularly spaced. We then analyze the case in which the traps are in fixed but random positions and show that the long-time decay of the ligand distribution is of the fractional exponential form N(t) ≅ N0 exp{-(tτ)35} for a three-dimensional system. We briefly discuss the consequences of this new point of view for the interpretation of the experiments.