The unfavorable scaling of wavefunction storage severely impacts the feasibility of quantum dynamical calculations in the condensed phase. Feynman’s path integral formulation offers an attractive alternative, replacing wavefunctions by a sum of quantum mechanical amplitudes along all possible paths. However, the path sum involves astronomical numbers of terms, and stochastic methods are unable to deal with the oscillatory quantum phase.<br/>A series of developments have led to efficient real-time path integral methods for a variety of processes. The quasi-adiabatic propagator path integral (QuAPI) for system-bath dynamics achieves linear scaling with the number of time steps by propagating a tensor that spans the memory interval. Recent work showed that one can further disentangle the variables through the small matrix decomposition of the path integral (SMatPI), thereby enabling the simulation of long-memory processes and multistate systems.  A different decomposition leads to the modular path integral (MPI) for extended systems, which allows the inclusion of any number of finite-temperature vibrational modes and scales linearly system length.  In addition to these numerically exact methods, the quantum-classical path integral (QCPI) offers a rigorous formulation of nonadiabatic dynamics in solution or biological environments.<br/>These methods are used to investigate quantum coherence and its destruction in charge, proton, and energy transfer processes in a variety of systems, as well as the dynamics of coupled qubits. Besides generating the populations and coherences of electronic/spin states over a range of temperatures, the simulations track the evolution of electronic-vibrational densities, vibrational amplitudes and mode energies, which offer a clear picture of nonadiabatic dynamics and mode-mode interactions in these systems. Various applications will be presented.

Real time path integral methods for condensed phase quantum dynamics

ACS Fall 2021

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