Quantum Monte Carlo dynamics: The stationary phase Monte Carlo path integral calculation of finite temperature time correlation functions

We present a numerically exact procedure for the calculation of an important class of finite temperature quantum mechanical time correlation functions. The present approach is based around the stationary phase Monte Carlo (SPMC) method, a general mathematical tool for the calculation of high dimensional averages of oscillatory integrands. In the present context the method makes possible the direct numerical path integral calculation of real-time quantum dynamical quantities for times appreciably greater than the thermal time (βℏ). Illustrative applications involving finite temperature anharmonic motion are presented. Issues of importance with respect to future applications are identified and discussed.