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Diffusion in classical periodic systems: The Smoluchowski equation approach

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  • Ferrando, R.
  • Spadacini, R.
  • Tommei, G.E.
  • Levi, A.C.

Abstract

The classical diffusion of a particle in a periodic system is studied employing the Smoluchowski equation with an external periodic field of force. Assuming a two-dimensional rectangular symmetry and an external potential of a simple cosine shape, the resulting eigenvalue problem leads to a Hill equation, which is solved numerically. The dynamic structure factor and its full width at half maximum (fwhm) are calculated up to large values of the momentum transfer extending in several Brillouin zones. It is shown that, decreasing the amplitude of the potential, the Smoluchowski equation describes a diffusive process which changes continuously from a jump to a liquid-like regime, with an intermediate behaviour which has some characteristics of both. In this context, recent scattering experiments on systems (premelting surfaces and absorbed monolayers) which seem to show such a behaviour, are briefly discussed.

Suggested Citation

  • Ferrando, R. & Spadacini, R. & Tommei, G.E. & Levi, A.C., 1991. "Diffusion in classical periodic systems: The Smoluchowski equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 141-154.
    • Handle: RePEc:eee:phsmap:v:173:y:1991:i:1:p:141-154
    DOI: 10.1016/0378-4371(91)90255-B
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    References listed on IDEAS

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    1. Festa, R. & d'Agliano, E.Galleani, 1978. "Diffusion coefficient for a Brownian particle in a periodic field of force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 90(2), pages 229-244.
    2. Matthöfer, Hans & Stoltenberg, Gerhard & Nölling, Wilhelm, 1980. "Finanzpolitik im Dilemma," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 60(5), pages 215-225.
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    Cited by:

    1. Mazroui, M. & Boughaleb, Y., 1996. "Interacting Brownian particles in a two dimensional periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(1), pages 93-107.
    2. Caratti, G. & Ferrando, R. & Spadacini, R. & Tommei, G.E., 1997. "An analytical approximation to the diffusion coefficient in overdamped multidimensional systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 115-131.

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