Dimensional dependence of the Stokes-Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violati...

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Bibliographic Details
Published in:The Journal of chemical physics 2013-10, Vol.139 (16), p.164502-164502
Main Authors: Charbonneau, Benoit, Charbonneau, Patrick, Jin, Yuliang, Parisi, Giorgio, Zamponi, Francesco
Format: Article
Language:English
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Summary:We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension d(u) = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4825177