Time correlation functions for finite systems using second-quantized molecular time scale generalized Langevin equation theory: Effect of rotating wave approximation

Abstract

Second-quantized molecular time scale generalized Langevin equation (MTGLE) theory is applied to the computation of time correlation functions for a finite system and shown to be convergent as a function of temperature and nonlinear coupling parameter. The system chosen is a simple nonlinear or quartic oscillator in which the rotating wave approximation has been made. The effect of this approximation in the context of an MTGLE approach to computing dipole spectra is explored. As a consequence of these computations, a new pathology of the MTGLE approach is uncovered; namely, coupling frequencies ω4cn can become negative. A procedure for dealing with this problem is demonstrated and shown to work successfully.