Anomalous diffusion with absorbing boundary

In a very long Gaussian polymer on time scales shorter than the maximal relaxation time, the mean squared distance traveled by a tagged monomer grows as approximately t(1/2) . We analyze such subdiffusive behavior in the presence of one or two absorbing boundaries and demonstrate the differences between this process and the subdiffusion described by the fractional Fokker-Planck equation. In particular, we show that the mean absorption time of diffuser between two absorbing boundaries is finite. Our results restrict the form of the effective dispersion equation that may describe such subdiffusive processes.