The importance of introducing a waiting time for Lattice Monte Carlo simulations of a polymer translocation process

For a standard Lattice Monte Carlo (LMC) simulation of a random walker subject to a bias, it is impossible to obtain both a correct mean velocity and diffusion coefficient. To correct this, a modified LMC algorithm has been developed where the introduction of a probability of remaining in the current state allows for a distribution of intervals between jumps. In this paper, we demonstrate the impact of this modification for a first-passage problem: the translocation of a polymer through a nanopore. We find that while either approach yields the correct mean first-passage time, the incorporation of a waiting time is necessary to obtain the correct spread of times.