Abstract :
This communication is inspired by recent results on the observation of “giant” rates for proton transfer in rutile TiO2 at low temperatures in pump-probe experiments. An important point is that this is not a tunneling effect. We show that this classical looking effect has a quantum mechanical origin and may be called lattice-assisted hopping. To explore the possibility of formulating transport properties in terms of mode vibrations, we use a “quantum” fluctuation–dissipation theorem, thus providing a concept of dynamic activation energy for ion hopping, which had been used in the above experimental study, rather heuristically, to fit the low-temperature “over the barrier” motion data. The resulting expression of hopping activation energy is more general than the standard one defined in units of k B T and is able to describe the crossover from the high to low-temperature regime of proton jumps.
