Two-bath model for activated surface diffusion of interacting adsorbates

Abstract

The diffusion and low vibrational motions of adsorbates on surfaces can be well described by a purely stochastic model, the so-called interacting single adsorbate model, for low-moderate coverages ͑ Շ 0.12͒. Within this model, the effects of thermal surface phonons and adsorbate-adsorbate collisions are accounted for by two uncorrelated noise functions, which arise in a natural way from a two-bath model based on a generalization of the one-bath Caldeira-Leggett Hamiltonian. As an illustration, the model is applied to the diffusion of Na atoms on a Cu͑001͒ surface with different coverages.

Quantum Zeno and anti-Zeno effects in surface diffusion of interacting adsorbates

“…The Caldeira-Leggett Hamiltonian model has also been used to describe the diffusion dynamics, representing the surface as an infinite collection of harmonic oscillators at a given surface temperature T (reservoir) and with an Ohmic (constant) friction (one-bath model [6]). If interacting adsorbates are considered, the total friction splits up into two contributions, η = γ + λ, as shown by means of the so-called interacting single adsorbate (ISA) approximation, which has been applied with success at low and intermediate coverages (two-bath model [7,8]). Within this model, γ is associated with the substrate or reservoir, while λ represents a collisional friction due to the collisions among adsorbates, thus being connected with the surface coverage.…”

Adsorbate surface diffusion: The role of incoherent tunneling in light particle motion

“…The scenario of several loss mechanisms discussed at the end of the previous section readily arises when considering the fact that diffusion by tunneling is actually affected by surface coverage [1]. In order to analyze this effect as well as to corroborate the previous friction coefficients, an alternative fitting is considered by using a temperature-dependent, collisional-friction model, namely the so-called two-bath model [16][17][18]. More specifically, this model has been considered to accomplish two purposes: (1) to corroborate the fitting values of the friction parameters obtained with the Grabert-Weiss theory, and (2) to determine the effect of low coverages on tunneling rates.…”

“…Accordingly, the total friction, now denoted by η, is a sum of two contributions: the usual substrate friction, γ, and a collisional friction, λ, accounting for collisions among adsorbates (η = γ + λ). For a convenient and simple analytical estimate of the λ dependence on the coverage and temperature, a simple hard-sphere model (even though we are well aware that the dependence might be much more complex) leads to a collisional friction given by [17] …”

“…In order to study the dependence of the tunneling rate with the surface coverage and therefore the collisional friction, we have also considered a second two-bath model [16][17][18], valid for moderate coverages. According to this model, the tunneling rate increases as coverage decreases.…”

“…More specifically, we have been able to extract friction coefficients for the two adsorbed species considered in the experiment, namely H and D. The values obtained are in consonance with the isotopic effect (γ D is about a factor two smaller than γ H ) as well as with those reported in the literature for other species [15], which are of the order of picoseconds. Furthermore, in order to investigate the effects of the surface coverage on tunneling diffusion, and corroborate the friction coefficients extracted from the fitting procedure, we have also carried out an alternative analysis by means of a temperature-dependent, collisional-friction model [16][17][18], shown to be valid at low coverages (as it is the case of the experiment, where θ = 0.1 ML, and below). In this model (the so-called two bath model), the adsorbate undergoes a total friction resulting from the sum of two contributions, namely the usual substrate friction plus a collisional friction accounting for the collision among adsorbates.…”