Exploiting memory in event-based simulations

Few simulation methods have succeeded in sampling efficiently the phase space of complex systems with a dynamics dominated by activated events. In order to address this limitation, we have recently introduced an activated algorithm based on a mixture of the activation-relaxation technique and molecular dynamics (the properly obeying probability activation relaxation technique, POP-ART). We show here that the basic implementation of POP-ART is only as fast as MD in sampling the phase space of a complex material, amorphous silicon at 600 K. However, as the activation moves are locally defined, it is possible to use a number of tricks that can increase significantly sampling efficiency of POP-ART. We consider an approach, the memory kernel, based on avoiding recently encountered moves and show using a simple model that this introduces very little bias while ensuring a significant gain over standard Monte Carlo in sampling the phase space of this model. Incorporating the memory kernel into POP-ART improves considerably its efficiency in sampling the phase space of amorphous silicon as compared to standard POP-ART and molecular dynamics.