Parsing the Influence Functional: Harmonic Bath Mapping and Anharmonic Small Matrix Path Integral

The influence functional (IF) encodes all of the information required for calculating the dynamical properties of a system in contact with its environment. A direct and simple procedure is introduced for extracting from a few numerical evaluations of the IF, without computing time correlation functions or evaluating integrals, the parameters required for path integral calculations, either within or beyond the harmonic mapping, and for assessing the accuracy of the harmonic bath approximation. In addition, the small matrix decomposition of the path integral (SMatPI) is extended to anharmonic environments and the required matrices are constructed directly from the IF.