Interacting particles crossing barriers: spatial statistics, choice of route taken and role of interactions
We consider the statistics of pairs of particles moving in a potential energy landscape exhibiting a choice of different pathways from a local minimum start point to the global energy minimum destination. We examine the impact of both attractive and repulsive interactions between the particles, treating these via either a soft Gaussian or a Lennard-Jones potential. We investigate the statistics of which particle arrives at the destination first, arrival-time distributions and where in the system the second particle is located when the first arrives. We find that the typical arrival time of the first particle can be significantly different to that of a single particle, sometimes being much longer and in other cases being shorter, depending on the nature of the particle interactions. In the case of soft Gaussian attractive interactions, which effectively bind the pair of particles together to form a single larger particle, the arrival time can be much longer, since bigger particles cross barriers more slowly. In contrast, the arrival time is shorter when there is a repulsive core interaction between the particles, due to excluded-area and particle-ordering effects. We investigate the probability distribution of particles' positions through the Jensen--Shannon divergence which unveils the dependence of the spatial distribution of the particles within the confining potential on the parameters of the particle interaction potentials.