Generalized Quantum Master Equation from Memory Kernel Coupling Theory

The generalized quantum master equation provides a powerful framework for non-Markovian dynamics of open quantum systems. However, the accurate and efficient evaluation of the memory kernel remains a challenge. In this work, we introduce a comprehensive tensorial extension to the memory kernel coupling theory (MKCT) to overcome this bottleneck. By elevating the original scalar formalism to a tensorial framework, the extended MKCT enables the calculation of general expectation values and cross-correlation functions. We demonstrate the numerical accuracy and efficiency of this method across multiple benchmark systems: capturing transient populations and coherences in the spin-boson model, resolving the excitonic absorption spectrum of the Fenna-Matthews-Olson complex, and simulating charge mobility in one-dimensional lattice models. These successful applications establish the tensorial MKCT as a highly efficient tool for investigating complex dynamics in open quantum systems.