A time-saving algorithm for generalized Langevin-dynamics simulations with arbitrary memory kernels

Abstract

A new algorithm for generalized Langevin-dynamics (GLD) simulations is presented. It is third-order (inclusive) in positions and requires the realization of only one stochastic trajectory. An approximate and very time-saving method is given to generate such trajectories in steps while still closely reproducing the original memory function. The algorithm, in conjunction with a rational evaluation of the friction force, is tested by simulating one krypton atom in dense liquid krypton in which the velocity autocorrelation function is non-trivial and exhibits a pronounced back-scattering minimum. The velocity autocorrelation function is at all times well reproduced and the algorithm is 10–20 times faster than other GLD algorithms.