Speeding up the first-passage for subdiffusion by introducing a finite potential barrier

Abstract

We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimised by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discus an improved deign for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation.