Spatial memory reveals exponentially slow onset of quantum diffusion of small polarons

Polarons—quasiparticles that consist of a charge excitation and the surrounding lattice distortion—serve as a primary carrier for transport across many semiconductors. While

minimal models capture small polaron formation and transport, exact quantum many-body dynamics in the strong carrier-phonon coupling regime remain a major challenge.

Numerically exact simulations are limited to short timescales and small system sizes due to exponential scaling, making it difficult to bridge nonequilibrium evolution and

thermodynamic behavior. We address this by developing a novel generalized master equation approach that leverages finite memory in time and space in dissipative lattice systems with short-range interactions. Using this framework, we show that nonequilibrium relaxation of polarons exhibits long-lived anomalous transport, transitioning into near-equilibrium diffusion only asymptotically in time and lattice size. This work advances the theoretical ability of performing polaron dynamics under experimentally relevant timescales and length scales and provides insights into how tuning the microscopic energy scales determines macroscopic mobilities.