Dimensional dependence of the Stokes-Einstein relation and its violation
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Date
2013-10-28
Authors
Charbonneau, Benoit
Charbonneau, Patrick
Jin, Yuliang
Parisi, Giorgio
Zamponi, Francesco
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Physics
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 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.
Description
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Charbonneau, B., Charbonneau, P., Jin, Y., Parisi, G., & Zamponi, F. (2013). Dimensional dependence of the Stokes–Einstein relation and its violation. The Journal of Chemical Physics, 139(16), 164502.and may be found at https://doi.org/10.1063/1.4825177
Keywords
Boundary value problems, Hydrodynamics, Glass transitions, Mean field theory, Solvents