First-passage distributions in a collective model of anomalous diffusion with tunable exponent.

We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes whose friction coefficients scale as wave number to the power 2-z. A single (tagged) monomer then executes subdiffusion over a broad range of time scales, and its mean square displacement increases as t(alpha) with alpha = 1/z. To demonstrate nontrivial aspects of the model, we numerically study the absorption of the tagged particle in one dimension near an absorbing boundary or in the interval between two such boundaries. We obtain absorption probability densities as a function of time, as well as the position-dependent distribution for unabsorbed particles, at several values of alpha. Each of these properties has features characterized by exponents that depend on alpha. Characteristic distributions found for different values of alpha have similar qualitative features, but are not simply related quantitatively. Comparison of the motion of translocation coordinate of a polymer moving through a pore in a membrane with the diffusing tagged monomer with identical alpha also reveals quantitative differences.