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

Abstract

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.

A temperature behavior of the frustrated translational mode of adsorbate and the nature of the “adsorbate–substrate” interaction

“…We will refer to the vibrational transitions with i = j, {i, j} = {L, R}, as the end-changing processes, supplying them afterwards by the subscript (c), and transitions with i = j will be termed as the end-preserving ones with the corresponding subscript (p). Using the method of the reduced density matrix [21] it is possible [16,19,20] to obtain the chain of quantum kinetic equations for diagonal f s,s (t) = i=L,R a † si a si t S and off-diagonal f s,s ′ (t) = i=L,R a † s ′ i a si t S one-particle non-equilibrium distribution functions, where the averaging is taken with the statistical operator ρ S (t) of the adsorbate. These integro-differential equations are linear in f s,s (t), f s,s ′ (t) but are non-local in time; hence it is useful to perform the Laplace transformationf (z) = ∞ 0 exp(−zt)f (t)dt.…”

“…These integro-differential equations are linear in f s,s (t), f s,s ′ (t) but are non-local in time; hence it is useful to perform the Laplace transformationf (z) = ∞ 0 exp(−zt)f (t)dt. Solving the equations for the offdiagonal distribution functions and inserting the obtained results into the equation for the diagonal ones, one can obtain [19,20] an expression for the generalized (frequency dependent) diffusion coefficient:…”

“…It can be interpreted [16,19] in terms of a simple model of bandtype motion limited by scattering from the lattice (with interatomic spacing a) at temperatures large relative to the bandwidth t inter , which is narrowed due to polaronic effect. The kinetic kernel…”

“…We explore a two-level model of the light particle coupled non-adiabatically to the surface phonons [18][19][20]. The other kinds of "adsorbate-substrate" interaction, like electronic friction or nonlinear phonon coupling, will be also considered.…”

“…In Sec. II we present the generalized diffusion coefficient of a light particle derived by the method of quantum kinetic equations [19,20] on the basis of two-level dissipative model of adparticle coupled to substrate phonons. In Sec.…”