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Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice

Henk van Beijeren 1Klaus W. Kehr 2Ryszard Kutner 3

1. Institute of Theoretical Physics, Utrecht University (ITPUU), Leuvenlaan 4, Utrecht 3584 CE, Netherlands
2. Institut fur Festkoerperforschungs, Forschungszentrum Jülich (FZJ), Wilhelm-Johnen-Straße, Jülich 52428, Germany
3. Faculty of Physics, University of Warsaw (FPUW), Pasteura 5, Warsaw 02-093, Poland

The dynamical process of the diffusion of tagged particles in a one-dimensional concentrated lattice gas is investigated. The particles are noninteracting except that double occupancy is forbidden. The mean-square displacement of a tagged particle is calculated for all times by an approximate theory and compared to results from Monte Carlo simulations. The overall agreement is quite good. For an infinite chain and for large time t the mean-square displacement is found to increase proportionally to t^{1/2} in agreement with existing results. For periodic chains it increases as 2D_{tr} t   for large times, with a coefficient of tracer diffusion D_{tr}  inversely proportional to the number of particles on the chain. This, too, is in agreement with the results of older calculations. In the case of hard reflecting walls finally the mean-square displacement asymptotically approaches a constant, which can be calculated simply.

Physical Review B 28, 5711 (1983).


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Presentation: Article at Econophysics group of Ryszard Kutner, by Ryszard Kutner
See On-line Journal of Econophysics group of Ryszard Kutner

Submitted: 2016-03-08 12:42
Revised:   2016-03-08 13:07