On the application of numerical analytic continuation methods to the study of quantum mechanical vibrational relaxation processes

A major problem still confronting molecular simulations is how to determine time-correlation functions of many-body quantum systems. In this paper the results of the maximum entropy ~ME! and singular value decomposition ~SVD! analytic continuation methods for calculating real time quantum dynamics from path integral Monte Carlo calculations of imaginary time time-correlation functions are compared with analytical results for quantum mechanical vibrational relaxation processes. This system studied is an exactly solvable system: a harmonic oscillator bilinearly coupled to a harmonic bath. The ME and SVD methods are applied to exact imaginary-time correlation functions with various level of added random noise, and also to imaginary-time data from path integral Monte Carlo ~PIMC! simulations. The information gathered in the present benchmark study is valuable for the application of the analytic continuation of PIMC data to complex systems. © 1998 American Institute of Physics. @S0021-9606~98!51340-2#