ABACUS Repository
Institutional repository of the Universidad Europea where the scientific production of its research community is collected. The purpose of the repository is to provide access and visibility to this work by gathering, preserving and disseminating this production.
Recent Submissions
Quantum-to-classical transition and H-theorem in surface diffusion
(2026) Torres Mirayes, Elena Esther; Miret Artés, Salvador
The so-called quantum-to-classical transition is studied in the surface diffusion dynamics. This continuous and smooth transition is carried out from the Liouville-von Neumann equation by scaling Planck’s constant. As an application, the Brownian motion of an adsorbate on a flat surface is analyzed within the Caldeira–Leggett master equation formalism for the reduced density matrix and the two extreme time behaviors, the ballistic and diffusive motions. In the ballistic time regime, the intermediate scattering function displays a Gaussian function which is governed by the thermal velocity in the classical regime, whereas in the quantum regime, by the initial spreading velocity of the wave packet. Adsorbates behave as a classical or quantum ideal gas. Finally, in the diffusive regime, and starting from the Chudley–Elliott model, the well-known H-function is calculated for three different surface temperatures in the diffusion of H and D on a Pt(111) surface. The main goal of this analysis is whether one can discriminate the irreversibility coming from tunneling or thermal activation diffusion.
The Characteristic Function as a Unifying Framework for Linear Response in Surface Diffusion
(2026) Torres Mirayes, Elena Esther; Mirtel Artés, Salvador
In this short perspective, we analyze the different linear response functions relevant to surface diffusion as studied by helium atom scattering, organizing them around a single object: the intermediate scattering function (ISF), which is also a characteristic function (CF) in the sense of probability theory. This organizing role of the CF is, to our knowledge, not made explicit elsewhere in the surface-diffusion literature. The exponential time dependence of the ISF observed in the diffusive regime (times much greater than the inverse of the friction coefficient) is a special case of the classical continuous-time random walk (CTRW) theory. Special emphasis is placed on this regime where quantum features of the diffusion process are washed out. We show how the entire hierarchy of response functions—the after-effect function, the generalized susceptibility, the relaxation function, and the Green function—can be written directly in terms of the time moments of the ISF at 𝑡=0. Moreover, the standard Pauli master equation and the Chudley–Elliott (CE) jump model follow as particular lattice realizations of a general compound-Poisson process. The extension to finite surface coverage is discussed within the interacting single adsorbate (ISA) model.
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