Is there a fractional breakdown of the Stokes-Einstein relation in Kinetically Constrained Models at low temperature?

Abstract : We study the motion of a tracer particle injected in facilitated models which are used to model supercooled liquids in the vicinity of the glass transition. We consider the East model, FA1f model and a more general class of non-cooperative models. For East previous works had identified a fractional violation of the Stokes-Einstein relation with a decoupling between diffusion and viscosity of the form $D\sim\tau^{-\xi}$ with $\xi\sim 0.73$. We present rigorous results proving that instead {$\log(D)/\log(\tau)\sim -1$} for very large time-scales. {Our result does not exclude the occurrence of SE breakdown, albeit non fractional. Indeed we believe that this violation occurs and our result suggests $D \sim\tau^{-1} 1/q^\alpha$, where $q$ is the density of excitations}\\ For FA1f we prove fractional Stokes Einstein in dimension $1$, and $D\sim\tau^{-1}$ in dimension $2$ and higher, confirming previous works. Our results extend to a larger class of non-cooperative models.
Type de document :
Article dans une revue
EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2014, 107, pp.26005. 〈10.1209/0295-5075/107/26005〉
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https://hal.archives-ouvertes.fr/hal-00843003
Contributeur : Oriane Blondel <>
Soumis le : mercredi 10 juillet 2013 - 10:03:23
Dernière modification le : jeudi 11 janvier 2018 - 06:12:29

Citation

Oriane Blondel, Cristina Toninelli. Is there a fractional breakdown of the Stokes-Einstein relation in Kinetically Constrained Models at low temperature?. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2014, 107, pp.26005. 〈10.1209/0295-5075/107/26005〉. 〈hal-00843003〉

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