Asymptotic laws for tagged-particle motion in glassy systems

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Physical Review E. 1998, 58(3), pp. 3384-3399. Available under: doi: 10.1103/PhysRevE.58.3384
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Within mode-coupling theory for structural relaxation in simple systems, the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These analytic results are compared with numerical ones of the equations of motion evaluated for a tagged hard sphere moving in a hard-sphere system. It is found that the long-time part of the two-step relaxation process for the mean-squared displacement can be characterized by the a-relaxation scaling law and von Schweidlers power-law decay, while the critical-decay regime is dominated by the corrections to the leading power-law behavior. For parameters of interest for the interpretations of experimental data, the corrections to the leading asymptotic laws for the non-Gaussian parameter are found to be so large that the leading asymptotic results are altered qualitatively by the corrections. Results for the non-Gaussian parameter are shown to follow qualitatively the findings reported in the molecular-dynamics-simulations work by Kob and Andersen [Phys. Rev. E 51, 4626 (1995)].

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ISO 690FUCHS, Matthias, Wolfgang GÖTZE, Matthias R. MAYR, 1998. Asymptotic laws for tagged-particle motion in glassy systems. In: Physical Review E. 1998, 58(3), pp. 3384-3399. Available under: doi: 10.1103/PhysRevE.58.3384
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@article{Fuchs1998Asymp-4875,
  year={1998},
  doi={10.1103/PhysRevE.58.3384},
  title={Asymptotic laws for tagged-particle motion in glassy systems},
  number={3},
  volume={58},
  journal={Physical Review E},
  pages={3384--3399},
  author={Fuchs, Matthias and Götze, Wolfgang and Mayr, Matthias R.}
}
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