Molecular dynamics algorithm for condensed systems with multiple time scales

A frequently encountered problem in molecular dynamics simulations is the long runs required to study condensed systems consisting of both high frequency and low frequency degrees of freedom. Standard integrators require the choice of time step sufficiently small to guarantee stable solution of the highest frequency motion with the consequence that simulations require a very large number of central processing unit (CPU) cycles. In this note we present a new integrator that allows one to use a time step appropriate for the low frequency degrees of freedom without making any approximations related to the separation of time scales. This method is based on a choice of an analytically solvable reference system for the high frequency motion. We show how the analytical solution can be incorporated into a numerical integrator. The method is applied to two cases which are paradigms for this problem and it is shown that this approach and suitable generalizations should be very useful for future simulations of quantum and classical condensed matter systems.