Simulation of rare events using nonequilibrium processes

Abstract

With the increasing availability of computational resources and due to the continuous improvement of computational methods, Computational Physics has become a crucial component of Condensed-Matter Physics, serving as a connection between pure theory and experiment. In this context, atomistic simulation techniques such as Molecular Dynamics (MD) and Monte Carlo (MC) play a particularly important role in the characterization of fundamental atomic processes that control the macroscopic properties of complex systems. This characterization is a common goal to many areas of Science, including Chemistry, Physics, Biology, and Materials Science, where a fundamental understanding of elementary processes requires detailed knowledge of the configurations and dynamics on the atomic scale. From this point of view, atomistic simulation represents a powerful tool that allows observation of the evolution of nanoscale structures throughout controlled computational "experiments". In this respect, atomistic simulation can serve as an alternative if an experiment in a conventional laboratory is considered difficult or even impossible. In spite of these strengths, the applicability of the atomistic simulation methods suffers from a fundamental limitation that can be attributed to the nature of the atomic scale, restricting the time scales accessible to this type of modeling. Since atomistic techniques operate on the natural time scale of atomic motion (for example, dictated by a typical frequency of phonon in the case of a solid), the maximum duration of a simulation is quite short, usually of the order of peak/nanoseconds. Furthermore, since the evolution of time of an atomistic system is typically described by a set of first-order differential equations with initial conditions (such as Newton's equations), it can not be parallelized. This implies that atomistic techniques are very inefficient in the handling of processes that are controlled by rare events: infrequent but dominant occurrences that control processes such as chemical reactions, nucleation processes, and defect movement in solids. In this direct doctoral project we will address the theme of rare events in atomistic simulations, focusing in particular on techniques based on nonequilibrium processes. (AU)