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

Abstract

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.

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:…”

“…The "adsorbate-substrate" interaction enters the kinetic rates via spectral weight functions [16,[18][19][20] …”

“…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.…”