On the Bayesian approach to calculating time correlation functions in quantum systems; reaction dynamics and spectroscopy

Abstract

We assess the current status, advantages and limitations of the numerical analytic continuation approach to computing time correlation functions in large many-body quantum systems characteristic of condensed phase chemical processes. We determine the quantum correlation function as a function of complex time, and use its analytic properties to select a suitable contour in the complex time plane along which the function can be evaluated efficiently by stochastic simulation methods. The simulation data are then used to obtain the values of the correlation function along the real-time axis through a maximum entropy numerical analytic continuation procedure. This approach is used to compute the dynamical properties of several condensed phase processes including vibrational relaxation lineshapes and canonical reaction rates. We discuss how to improve the accuracy of the numerical analytic continuation methods.