Small Matrix Quantum-Classical Path Integral

The quantum-classical path integral (QCPI) is a rigorous formulation of nonadiabatic dynamics, where the dynamical interaction between a quantum system and its environment is captured consistently through classical trajectories driven by forces along quantum paths of the system. In this Letter, we develop a small matrix decomposition (SMatQCPI) that eliminates the tensor storage requirements of the iterative QCPI algorithm. In the case of a system coupled to a harmonic bath, SMatQCPI provides fully quantum mechanical propagation, which also reduces the computational cost to that of a single QCPI step. Further, the SMatQCPI matrices only need to account for quantum contributions to decoherence, allowing high efficiency in challenging regimes of incoherent dynamics. Overall, this new composite algorithm combines the best features of two powerful path integral formulations and offers a versatile tool for simulating condensed phase quantum dynamics.