A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches.

Velocity autocorrelation functions (VAFs) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have a purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the molecular dynamic data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode theory, the mode coupling theory, and some other theoretical approaches.

A temperature behavior of the frustrated translational mode of adsorbate and the nature of the "adsorbate-substrate" interaction.

A temperature behavior of the frustrated translational mode (T-mode) of a light particle, coupled by different regimes of ohmicity to the surface, is studied within a formalism of the generalized diffusion coefficients. The memory effects of the adsorbate motion are considered to be the main reason of the T-mode origin. Numerical calculations yield a thermally induced shift and broadening of the T-mode, which is found to be linear in temperature for Ohmic and super-Ohmic systems and nonlinear for strongly sub-Ohmic ones. We obtain analytical expressions for the T-mode shift and width at weak coupling for the systems with integer "ohmicity" indexes n = 0÷2 in zero temperature and high temperature limits. We provide an explanation of the experimentally observed blue- or redshifts of the T-mode on the basis of a comparative analysis of two typical times of the system evolution: a time of decay of the "velocity-velocity" autocorrelation function, and a correlation time of the thermal bath random forces. A relation of the T-mode to the multiple jumps of the adsorbate is discussed, and generalization of conditions of the multiple hopping to the case of quantum surface diffusion is performed.

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, 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 temperature T and vibrational frequency Ω. These domains are found to coincide with the regions where the experimentally observed diffusion coefficients change their behavior from weakly dependent on T to quite a sensitive function of the temperature. We also evaluate the off-diagonal 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.

Kinetic equation approach to the description of quantum surface diffusion: non-Markovian effects versus jump dynamics.

We consider surface diffusion of a single particle, which performs site-to-site underbarrier hopping, fulfils intrasite motion between the ground and the first-excited states within a quantum well, and interacts with surface phonons. We obtain a chain of quantum-kinetic equations for one-particle distribution functions and nonequilibrium hopping probabilities. The generalized diffusion coefficients are derived, and the generic non-Markovian diffusion equation is written down both for the infinite lattice model and in the continuous media limit. In the latter case, the one-particle distribution function obeys the telegrapher's equation, which could give us a nonmonotonic behavior of the intermediate distribution functions at large spatial gradients. In a weak-coupling limit, if the energy of level splitting is comparable with the temperature, there are also pronounced oscillations of the generalized diffusion coefficients. The recrossing/multiple crossing phenomena, a problem of long tails of the generalized diffusion coefficients, as well as a mapping into the next- to the nearest-neighbors hopping regime, are discussed.