Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results

• Published in: Condensed Matter Physics
• Date: 2010
• Main Authors: Ilyin, V., Procaccia, I., Zagorodny, A.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/32087
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results / V. Ilyin, I. Procaccia, A. Zagorodny // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 23001: 1-8. — Бібліогр.: 19 назв. — англ.

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly re...