Asymptotic behavior of self-affine processes in semi-infinite domains

Zoia, Andrea; Rosso, Alberto; Majumdar, Satya N.

Asymptotic behavior of self-affine processes in semi-infinite domains

Authors

Zoia, Andrea

Rosso, Alberto

Majumdar, Satya N.

Description

We propose to model the stochastic dynamics of a polymer passing through a pore (translocation) by means of a fractional Brownian motion, and study its behavior in presence of an absorbing boundary. Based on scaling arguments and numerical simulations, we present a conjecture that provides a link between the persistence exponent $θ$ and the Hurst exponent $H$ of the process, thus sheding light on the spatial and temporal features of translocation. Furthermore, we show that this conjecture applies more generally to a broad class of self affine processes undergoing anomalous diffusion in bounded domains, and we discuss some significant examples.
4 pages, 3 figures; to be published in Phys. Rev. Lett