Dynamical processes in the condensed phase: methods and models

In this thesis, we study a broad range of physical phenomena from the perspectives of theory-driven, and machine learning models. We begin by introducing a generalization of the Momentum Average method for finding numerically exact Green's functions of arbitrary polaron systems at zero and finite temperature. This method utilizes the physical ansatz that phonons are produced largely in clouds, and systematically constructs a closure of auxiliary Green's functions to ultimately solve for the spectrum. We seamlessly apply this method to a variety of problems, including the Holstein, Peierls, and mixed-boson mode models. Next, we leverage fundamental quantum mechanics to develop a microscopic model of exciton and trion scattering in monolayer transition metal dichalcogenides. We conclude that elastic scattering mechanisms are largely the dominant contributor, and confirm that our calculated doping-dependent linewidths qualitatively agree with experiment. In addition, we use Monte Carlo dynamics to examine entropically activated dynamics in continuous phase space models, and show that global and local dynamics both exhibit entropy driven activation. The second type of work discussed in this thesis pertains to data-driven machine learning models. These approaches offer the utility of instantaneous inference, which has tremendous potential application in applied science in areas such as surrogate modeling and creating digital twins of expensive experiments. First, we demonstrate that x-ray absorption spectra can be used to classify absorbing sites' local atomic information, specifically its coordination number. Next, we show that graph-based neural networks can to quantitative accuracy, predict the x-ray absorption spectrum of small molecules in the QM9 database. We highlight the various ways in which these types of methodologies can be applied to e.g. closing the design loop and surrogate modeling in general