One-Dimensional Random Walk in Multi-Zone Environment
arXiv:1610.08046 · doi:10.1088/1751-8121/aa6466
Abstract
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be differently fixed. We derive analytically the probability to find a walker at the given position and time. The probability distribution function is found and has no Gaussian form because of properties of adsorption in the bulk of zones and partial reflection at the separation points. Time dependence of the mean squared displacement of a walker is studied as well and revealed the transient anomalous behavior as compared with ordinary RW.
12 pages, 2 figures
References in corpus (6)
- Anomalous transport in the crowded world of biological cells
- Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
- Random walk with barriers: Diffusion restricted by permeable membranes
- Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects
- Scaling Green-Kubo relation and application to three aging systems
- Position-dependent mass, finite-gap systems, and supersymmetry