  We present a hybrid quantum-classical simulation of charge-polaron transport
in conjugated polymers. The charge, which couples to the angular rotations of
the monomers, is modeled via the time-dependent Schr\"odinger equation, while
the monomers are treated classically via the Ehrenfest equations of motion. In
addition, the system is thermalized by assuming that the monomers are subject
to Brownian fluctuations modeled by the Langevin equation. Charge coupling to
the monomer rotations localizes the particle into a Landau polaron, while the
thermal fluctuations of the monomers causes polaron dynamics. The emergent
low-energy scale of the model is the polaron reorganization energy, $E_r$, and
thus $T_r = E_r/k_B$ is a convenient scale for the low-temperature dynamics. We
investigate two types of dynamics -- both relevant for temperatures $T < T_r$.
In the lower temperature regime the system remains in the same quasidiabatic
state, corresponding to activationless polaron diffusion as the polaron crawls
stochastically along the chain. As the temperature is raised, however, there is
a cross-over to an additional activated transfer process which corresponds to
hopping between diabatic states. We show that these processes exhibit
Landau-Zener type dynamics. We note that as our model is general, it equally
applies to exciton-polaron (i.e., energy) transport in conjugated polymers, and
to charge and exciton polaron transport in quasi one-dimensional molecular
stacks.
