Methods for simulating time correlation functions in quantum systems

Abstract

A review of the basic strategies that we have developed for the simulation of dynamic correlation functions in quantum systems is provided. Three methods are considered: (a) the analytic continuation of imaginary (thermal) time correlation functions to real times; (b) direct evaluation of thermally symmetrized version of the time correlation functions; (c) direct simulation of the power spectrum. All of these methods are based on the path integral representation of time corellation functions. The generalization of these methods for the computation of electronic spectrum, which involves the consideration of two potential energy surfaces, is also presented. We also discuss the approach based on numerical integration of an effective time-dependent Schrödinger equation for the simulation of electronic absorption and emission spectra for mixed quantum classical systems.