Fast power law-like decay for a diffusive system with absorbing borders

Using a simple, one dimensional, model of diffusing particles which are absorbed at the ends of the system, we compare two ways of updating in the Monte Carlo simulations. In the first one particles at each Monte Carlo step are chosen randomly, while in the second one we follow at each Monte Carlo Step a list of particles made at the beginning of simulations, in which there is no correlation between the position of a particle on the list and its spatial location. We show that although the final state is the same-the empty state, the two approaches follow quite different ways to the final state. In the first one the density of particles decreases exponentially with time, while in the second one it has a power-type character. An additional feature which is different in the two approaches is the direction of the average movements of the particles. In the first case they are moving away from the edges, towards the centre, while in the second case the average jumps are towards the edges. We have no good explanation for the observed differences and leave them as open questions.