Real-Time Path Integral Methodology for Quantum Dynamics in Condensed-Phase Environments

Since the mid-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 iterative propagation with matrices of minimal 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. Combination with modular path integral (MPI) decompositions suitable to systems with a locally one-dimensional topology enables iteration in space and time, leading to linear scaling with system size and propagation length. The methodology has been extended to anharmonic environments, whose effects on the RDM can be equivalent to those from an effective harmonic bath or give rise to novel features arising from essential, non-removable anharmonicity. Recent work has shown that the quantum paths entering the path integral expression can be mapped on graphs, whose properties can be exploited to arrive at novel algorithms that allow the efficient treatment of static disorder and the simulation of processes that involve thousands of system states (regardless of the nature of the system Hamiltonian).

Speaker: Nancy Makri, University of Illinois