# 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00843003
Contributor : Oriane Blondel <>
Submitted on : Wednesday, July 10, 2013 - 10:03:23 AM
Last modification on : Saturday, March 28, 2020 - 2:08:04 AM

### 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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