Abstract
Simulating physical processes in complex systems such as slowly relaxing glassy systems and biomolecules in solution often involves investigating dynamics at long time scales. Typically, simulations are performed by numerically propagating the equations of motion over discrete time intervals that have to be small enough (usually on the order of femtoseconds) to get stable and realistic dynamics. Thus, a large number of iterations is required to reach physically relevant time scales. As an alternative, one can approximate the dynamics by
replacing the continuous potential by a discretized version consisting of steps at which the potential energy changes instantaneously. For such a system, the dynamics consists of free flights punctuated by interaction events, both of which are analytically solvable for point particles and rigid bodies. The method is demonstrated on several model systems, among which methane, benzene and polar molecules. It is found that even when the interaction times have to be determined numerically, discontinuous molecular dynamics simulations are more
efficient than their continuous counterparts without loss of the essential physics, while having excellent long-term stability properties.
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