Anomalous Diffusion with an Absorbing Wall

Fractional Brownian Motion and the Fractional Langevin Equation, random processes characterized by long-time power law correlations in the noise, are prototypical models for anomalous diffusion. We employ large scale Monte Carlo simulations to investigate these models in the presence of an absorbing wall. In the limit of vanishing correlations, our findings reproduce the well-known results for normal diffusion. In contrast, the interplay between the absorbing wall and the long-range power correlations leads to a singular probability density close to the wall. We compare our results to those of Fractional Brownian Motion [1] as well as the Fractional Langevin Equation [2] in the presence of a reflecting wall, and we discuss implications of our results.
[1] A.H.O Wada and T. Vojta, Phys. Rev. E 97, 020102 (2018)
[2] T. Vojta, S. Skinner, R. Metzler, arXix:1907.08188