Generalized Brownian dynamics. I. Numerical integration of the generalized Langevin equation through autoregressive modeling of the memory function

A method is presented for numerical integration of the generalized Langevin equation (GLE) based on modeling of the ‘‘random force’’ as a discrete autoregressive process. This modeling procedure, drawn from digital signal processing and spectral estimation methods which have been used extensively in electrical engineering applications, provides for efficient evaluation of the friction integral in the GLE as well as for generation of a random force process with the desired spectrum. The method is shown, through comparison with molecular dynamics results, to be effective in simulating the force autocorrelation function of an iodine atom dissolved in Lennard-Jones (LJ) xenon. In a companion paper this method is applied in a simulation of the vibrational relaxation of I2 in LJ xenon at two very different densities and found to perform well.