Local Determinacy of Quantum Master Equations and a Mechanical Interpretation of the Multi-Mode Jaynes-Cummings and Central Spin Models

We propose a novel formulation of master equations for open systems wherein the evolution of a state is determined solely by its local behaviour at any point of time. Specifically, our formulation allows for a local interpretation of the workings of beyond-Markovian dynamics as opposed to the more common conception that non-Markovian state evolution is affected by its cumulative past history. Quite interestingly, local determinacy is found prevalent in quantum dynamics. We illustrate the advantages of our coordinate-free formulation with exact analyses on two physically relevant models.