From subdiffusion to superdiffusion of particles on solid surfaces

A. M. Lacasta, J. M. Sancho, A. H. Romero, I. M. Sokolov, and K. Lindenberg
Phys. Rev. E 70, 051104 – Published 15 November 2004

Abstract

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

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  • Received 29 July 2004

DOI:https://doi.org/10.1103/PhysRevE.70.051104

©2004 American Physical Society

Authors & Affiliations

A. M. Lacasta1, J. M. Sancho2, A. H. Romero3, I. M. Sokolov4, and K. Lindenberg5

  • 1Departament de Física Aplicada, Universitat Politècnica de Catalunya, Avinguda Doctor Marañon 44, E-08028 Barcelona, Spain
  • 2Departament d’Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
  • 3Advanced Materials Department, IPICyT, Apartado Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP, Mexico
  • 4Institut für Physik, Humboldt Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany
  • 5Department of Chemistry and Biochemistry 0340, and Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0340, USA

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Issue

Vol. 70, Iss. 5 — November 2004

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