Energy drift in molecular dynamics simulations

In molecular dynamics, Hamiltonian systems of differential equations are numerically integrated using the Störmer–Verlet method. One feature of these simulations is that there is an unphysical drift in the energy of the system over long integration periods. We study this energy drift, by considering a representative system in which it can be easily observed and studied. We show that if the system is started in a random initial configuration, the error in energy of the numerically computed solution is well modeled as a continuous-time stochastic process: geometric Brownian motion. We discuss what in our model is likely to remain the same or to change if our approach is applied to more realistic molecular dynamics simulations.