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Coherence, decoherence, and memory effects in the problems of quantum surface diffusion

We consider surface diffusion of a single particle, which performs site-to-site under-barrier hopping, fulfils intrasite motion between the ground and the first excited states within a quantum well, and interacts with surface phonons. On the basis of quantum kinetic equations for one-particle distribution functions obtained earlier we study the coherent and incoherent motion of the adparticle. In the latter case we derive the generalized diffusion coefficients and study various dynamic regimes of the adparticle. The critical values of the coupling constant $G_{cr}(T,Ω)$, which separate domains with possible recrossing from those with the monotonic motion of the adparticle, are calculated as functions of a temperature $T$ and a vibrational frequency $Ω$. These domains are found to coincide with the regions where the experimentally observed diffusion coefficients change its behavior from weakly dependent on $T$ to quite a sensitive function of the temperature. We also evaluate the off-diagonal (relative to the site labels) distribution functions both in the Markovian limit and when the memory effects become important. The obtained results are discussed in the context of the "long tails" problem of the generalized diffusion coefficients, the recrossing/multiple crossing phenomena, and an eventual interrelation between the adparticle dynamics at short times and the temperature dependence of the diffusion coefficients measured experimentally.