| Full text | |
| Author(s): |
Wada, Alexander H. O.
;
Warhover, Alex
;
Vojta, Thomas
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. N/A, p. 20-pg., 2019-03-01. |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 17/08631-0 - Nonequilibrium phase transitions in the presence of temporal disorder |
| Grantee: | Alexander Hideki Oniwa Wada |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |