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Article

Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime

1
Facultad de Física, Universidad de La Habana, San Lázaro y L, Vedado, La Habana 10400, Cuba
2
Instituto Superior de Tecnologías y Ciencias Aplicadas (InSTEC), Universidad de La Habana, Avenida Salvador Allende No. 1110, Entre Boyeros e Infanta, Plaza, La Habana 10400, Cuba
3
Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain
*
Author to whom correspondence should be addressed.
Academic Editors: Pedro Fernández de Córdoba, Juan Carlos Castro and Miguel Ángel García March
Mathematics 2021, 9(4), 362; https://doi.org/10.3390/math9040362
Received: 21 January 2021 / Revised: 5 February 2021 / Accepted: 8 February 2021 / Published: 11 February 2021
Stochastic wave function formalism is briefly introduced and applied to study the dynamics of open quantum systems; in particular, the diffusion of Xe atoms adsorbed on a Pt(111) surface. By starting from a Lindblad functional and within the microscopic Caldeira–Leggett model for linear dissipation, a stochastic differential equation (Ito^-type differential equation) is straightforwardly obtained. The so-called intermediate scattering function within the ballistic regime is obtained, which is observable in Helium spin echo experiments. An ideal two-dimensional gas has been observed in this regime, leading to this function behaving as a Gaussian function. The influence of surface–adsorbate interaction is also analyzed by using the potential of two interactions describing flat and corrugated surfaces. Very low surface coverages are considered and, therefore, the adsorbate–adsorbate interaction is safely neglected. Good agreement is observed when our numerical results are compared with the corresponding experimental results and previous standard Langevin simulations. View Full-Text
Keywords: LINDBLAD approach; Caldeira–Leggett master equation; stochastic differential equation; stocastic wave functions; intermediate scattering function; ballistic regime LINDBLAD approach; Caldeira–Leggett master equation; stochastic differential equation; stocastic wave functions; intermediate scattering function; ballistic regime
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MDPI and ACS Style

Torres-Miyares, E.E.; Rojas-Lorenzo, G.; Rubayo-Soneira, J.; Miret-Artés, S. Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime. Mathematics 2021, 9, 362. https://doi.org/10.3390/math9040362

AMA Style

Torres-Miyares EE, Rojas-Lorenzo G, Rubayo-Soneira J, Miret-Artés S. Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime. Mathematics. 2021; 9(4):362. https://doi.org/10.3390/math9040362

Chicago/Turabian Style

Torres-Miyares, E. E., G. Rojas-Lorenzo, J. Rubayo-Soneira, and S. Miret-Artés. 2021. "Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime" Mathematics 9, no. 4: 362. https://doi.org/10.3390/math9040362

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