Title: Path Integral Methods and Exciton-Vibration Dynamics
Abstract:
Since the early 1990s, the iterative, tensor-based quasi-adiabatic propagator path integral (QuAPI) methodology has enabled numerically exact, fully quantum mechanical simulations of system-bath dynamics. Recent work showed that one can further disentangle the path integral variables through the rigorous small matrix decomposition (SMatPI), which leads to expressions that involve a discrete convolution and thus have the structure of the generalized quantum master equation (GQME), with matrices of size equal to that of the system’s reduced density matrix (RDM). By eliminating tensor storage, the SMatPI algorithm enables the simulation of multistate systems and long-memory processes. A modular decomposition of the path integral (MPI) allows calculations in systems of many interacting system-bath units with effort that scales linearly with the number of units.
Besides generating the populations and coherences of electronic states over a range of temperatures, the path integral simulations track the evolution of electronic-vibrational densities, revealing the impact of individual and collective vibrational modes on charge and energy transfer, and have identified quantum mechanical signatures of regular and chaotic motion as well as intriguing topological phase effects. By grouping paths into equivalence classes, the path integral methods can be implemented for a large number of system Hamiltonians without additional cost, allowing the inclusion of time-dependent fields and static disorder. Further, the rich information content of the time-evolving RDM can be efficiently conveyed through coherence maps, which offer a powerful visualization tool for understanding the creation and destruction of quantum superpositions and enable a state-to-state pathway analysis of dynamical processes.
Recent work has extended these ideas to Hamiltonians that involve anharmonic baths, utilizing propagation matrices constructed by parsing the influence functional from the system’s environment. These methods allow the exploration of novel effects induced by essential bath anharmonicity, which cannot be captured by effective harmonic bath mappings.
Faculty Host: Prof. Yang Yang