Constant temperature molecular dynamics simulations by means of a stochastic collision model. II. The harmonic oscillator

Our recently introduced stochastic method for molecular dynamics simulations at constant temperature [J. Chem. Phys. 100, 566 (1994)] which is based on impulsive collisions between system particles and heat bath particles of finite masses, is extended and analyzed for the case of an ensemble of harmonic oscillators as a simple but theoretically solvable model for interacting systems. This model case can be considered, e.g., as a single normal mode of a polyatomic molecule. Both position space properties and velocity space properties are investigated. Analytical expressions for stationary probability densities and autocorrelation functions are derived. The effect of the truncation of the Taylor series which is the basis of Verlet-type algorithms, on the resulting temperature in position space and velocity space is quantitatively discussed. It is demonstrated that the system temperature in position space and in velocity space is controlled by complex parameter functions.