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American Institute of Physics, The Journal of Chemical Physics, 16(139), p. 164502

DOI: 10.1063/1.4825177

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Dimensional dependence of the Stokes–Einstein relation and its violation

Journal article published in 2013 by Benoit Charbonneau, Patrick Charbonneau, Yuliang Jin, Giorgio Parisi ORCID, Francesco Zamponi ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

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 du = 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.