Dimensional dependence of the Stokes-Einstein relation and its violation
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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. © 2013 AIP Publishing LLC.
Published Version (Please cite this version)10.1063/1.4825177
Publication InfoCharbonneau, Benoit; Charbonneau, Patrick; Jin, Y; Parisi, G; & Zamponi, Francesco (2013). Dimensional dependence of the Stokes-Einstein relation and its violation. Journal of Chemical Physics, 139(16). 10.1063/1.4825177. Retrieved from https://hdl.handle.net/10161/17096.
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Associate Professor of Chemistry
Professor Charbonneau studies soft matter. His work combines theory and simulation to understand the glass problem, protein crystallization, microphase formation, and colloidal assembly in external fields.