Open-quantum-system theory of non-Markovian electron-phonon dynamics

We present a non-Markovian open quantum dynamics formalism for the study of nonequilibrium electron-phonon interactions, based on a closed set of four coupled equations of motion for the electronic one-body reduced density matrix, the phonon density matrix, the coherent phonon, and the electron-phonon correlations. Memory effects in the electronic dynamics emerge naturally from the coupling between the electronic density matrix and the electron-phonon correlation equations, beyond the Markovian approximation. The formalism treats coherent-phonon dynamics and dissipative broadening on an equal footing, making it particularly suited to polaron formation and the finite lifetimes of driven electronic excitations. In appropriate limits it recovers the Fan-Migdal, polarization in random-phase-approximation, and Ehrenfest self-energies of nonequilibrium Green's function theory, as well as the Lindblad and Boltzmann equations, while avoiding the storage of two-time correlators. To drive the system out of equilibrium, we study its interaction with an external time-dependent field. As an illustrative application, we benchmark our theory against the exact solution of the Holstein dimer under a strong external perturbation, where the non-Markovian dynamics correctly captures dissipative spectral broadening and energy conservation.