A General Non-Markovian Electronic Friction and Langevin Dynamics Framework for Nonequilibrium Systems

Abstract

We present a general framework for simulating the nonequilibrium vibronic dynamics of molecules interacting with metal surfaces, which utilizes non-Markovian electronic friction and the corresponding generalized Langevin equation. The method employs a Markovian embedding scheme to sample coordinate-dependent quantum colored noise, with the underlying memory kernels represented systematically by exponential decompositions obtained directly from the electronic forces. In doing so, the approach extends the widely used electronic friction and Langevin dynamics formalism beyond the conventional Markovian approximation while retaining the coordinate dependence of the electronic back-action. We demonstrate the method for nonequilibrium charge transport through a vibrationally coupled molecular junction, where comparisons with numerically exact hierarchical equations of motion simulations show that the non-Markovian formulation is both more accurate and more robust than its Markovian counterpart. In particular, we find that non-Markovian electronic forces play a decisive role in the nonequilibrium vibrational dynamics, stabilizing regimes in which the conventional Markovian approximation fails.