  Predicting how a material's microscopic structure and dynamics determine its
transport properties remains a fundamental challenge. To alleviate this task's
often prohibitive computational expense, we propose a Mori-based generalized
quantum master equation (GQME) to predict the frequency-resolved conductivity
of small-polaron forming systems described by the dispersive Holstein model.
Unlike previous GQME-based approaches to transport that scale with the system
size and only give access to the DC conductivity, our method requires only one
calculation and yields both the DC and AC mobilities. We further show to easily
augment our GQME with numerically accessible derivatives of the current to
increase computational efficiency, collectively offering computational cost
reductions of up to $90\%$, depending on the transport regime. Finally, we
leverage our exact simulations to demonstrate the limited applicability of the
celebrated and widely invoked Drude-Smith model in small-polaron forming
systems. We instead introduce a cumulant-based analysis of experimentally
accessible frequency data to infer the microscopic Hamiltonian parameters. This
approach promises to provide valuable insights into material properties and
facilitate guided design by linking macroscopic terahertz measurements to the
microscopic details of small polaron-forming systems.
