期刊
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
卷 -, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/ab02f1
关键词
Brownian motion; diffusion; classical phase transitions
资金
- NSF [PHY-1125915, PHY-1607611, DMR-1506152, DMR-1828489]
- Sao Paulo Research Foundation (FAPESP) [2017/08631-0]
A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary increments, is a prototypical model for this situation. Here, we extend the previous results found for unbiased reflected fractional Brownian motion (Wada et al 2018 Phys. Rev. E 97 020102) to the biased case by means of Monte Carlo simulations and scaling arguments. We demonstrate that the interplay between the reflecting wall and the correlations leads to highly non-Gaussian probability densities of the particle position x close to the reflecting wall. Specifically, the probability density P(x) develops a power-law singularity P similar to x(kappa) with kappa < 0 if the correlations are positive (persistent) and kappa > 0 if the correlations are negative (antipersistent). We also analyze the behavior of the large-x tail of the stationary probability density reached for bias towards the wall, the average displacements of the walker, and the first-passage time, i.e. the time it takes for the walker reach position x for the first time.
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