Ultraslow diffusion in an exactly solvable non-Markovian random walk

Autor(es)

da Silva, M. A. A. ^[1] ; Viswanathan, G. M. ^[2] ; Cressoni, J. C. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, FCFRP, Dept Quim & Fis, BR-14040903 Ribeirao Preto - Brazil

^[2] Univ Fed Rio Grande do Norte, Dept Fis Teor & Expt, BR-59078900 Natal, RN - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Physical Review E; v. 89, n. 5 MAY 8 2014.
• Citações Web of Science: 11

Resumo

We study a one-dimensional discrete-time non-Markovian random walk with strong memory correlations subjected to pauses. Unlike the Scher-Montroll continuous-time random walk, which can be made Markovian by defining an operational time equal to the random-walk step number, the model we study keeps a record of the entire history of the walk. This new model is closely related to the one proposed recently by Kumar, Harbola, and Lindenberg {[}Phys. Rev. E 82, 021101 (2010)], with the difference that in our model the stochastic dynamics does not stop even in the extreme limit of subdiffusion. Surprisingly, this small difference leads to large consequences. The main results we report here are exact results showing ultraslow diffusion and a stationary diffusion regime (i.e., localization). Specifically, the equations of motion are solved analytically for the first two moments, allowing the determination of the Hurst exponent. Several anomalous diffusion regimes are apparent, ranging from superdiffusion to subdiffusion, as well as ultraslow and stationary regimes. We present the complete phase diffusion diagram, along with a study of the persistence and the statistics in the regions of interest. (AU)

• Processo FAPESP: 11/06757-0 - Processos difusivos: caminhantes aleatórios com memória
• Beneficiário: Marco Antonio Alves da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/13685-6 - Modelagem analítica e computacional de sistemas difusivos
• Beneficiário: Marco Antonio Alves da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil