Self-diffusion in simple models: Systems with long-range jumps |
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Authors: | A Asselah R Brito J L Lebowitz |
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Institution: | (1) Department of Mathematics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Departamento Fisica Aplicada I, Facultad de CC, Fisicas, Universidad Complutense, 28040 Madrid, Spain;(3) Department of Mathematics and Physics, Rutgers University, 08903 New Brunswick, New Jersey |
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Abstract: | We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self-diffusion coefficientD
N() in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set ofN neighboring sites. We obtain positive upper and lower bounds onF
N()=N{(1–)–DN()/DN(0)]}/(1–)]x for 0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest thatF
N becomes effectively independent ofN forN20. |
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Keywords: | Self-diffusion long-range jumps diffusion constant meanfield limit |
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