Some exact results for the trapping of subdiffusive particles in one dimension

TL;DR

This paper derives exact solutions for the survival probability of subdiffusive particles in one dimension with randomly distributed traps, using fractional diffusion theory and validating with simulations.

Contribution

It provides the first exact analytical results for trapping of subdiffusive particles in one dimension with random traps, extending classical trapping theory.

Findings

Exact survival probability formulas derived for subdiffusive particles

Good agreement between analytical results and simulations

Enhanced understanding of trapping dynamics in subdiffusive systems

Abstract

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is made