Generalized nonlinear Langevin equation for a rotor

A pendulum (rotor) coupled to a bath of harmonic oscillators is set up as a model for the dynamics of strongly coupled systems. The oscillators can be eliminated from the equation of motion for the rotor, except for initial conditions. The resulting Langevin equation is exact. Numerical solutions are provided for the power spectra of velocity and angular correlation functions of the pendulum for a broad range of the strength of the coupling starting from a weak coupling (hindered rotor) to the strong-coupling (‘‘free’’ rotor) limit, using both the rotor equation of motion and the full molecular dynamics.