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 wavenumber 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 tα with
α=1/z. To demonstrate non-trivial 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 α. Each of
these properties has features characterized by exponents that depend on
α. Characteristic distributions found for different values of α
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
α also reveals quantitative differences.Comment: LaTeX, 10 pages, 8 eps figure