Fractional Brownian motion with a reflecting wall

Autor(es)

Wada, Alexander H. O. ^{[1, 2]} ; Vojta, Thomas ^{[1, 3]}

Afiliação do(s) autor(es)

^[1] Missouri Univ Sci & Technol, Dept Phys, Rolla, MO 65409 - USA

^[2] Univ Sao Paulo, Inst Fis, Rua Matao 1371, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Calif Santa Barbara, Kavli Inst Theoret Phys, Santa Barbara, CA 93106 - USA

• Tipo de documento: Artigo Científico
• Fonte: Physical Review E; v. 97, n. 2 FEB 13 2018.
• Citações Web of Science: 13

Resumo

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior < x(2)> similar to t(alpha), the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case alpha > 1, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion alpha < 1, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events. (AU)

• Processo FAPESP: 17/08631-0 - Transições de fase fora do equilíbrio na presença de desordem temporal
• Beneficiário: Alexander Hideki Oniwa Wada
• Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Doutorado