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20 September 2020
 
  » arxiv » 1307.1651

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Is there a breakdown of the Stokes-Einstein relation in Kinetically Constrained Models at low temperature?
Oriane Blondel ; Cristina Toninelli ;
Date 5 Jul 2013
AbstractWe 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 $Dsim au^{-xi}$ with $xisim 0.73$. We present rigorous results proving that instead $Dsim au^{-1}$ at leading order for very large time-scales. Our results still suggest a violation but weaker, $D ausim 1/q^alpha$, where $q$ is the density of excitations. We discuss the expected value of $alpha$. For FA1f we prove fractional Stokes Einstein in dimension 1, and $Dsim au^{-1}$ in dimension 2 and higher, confirming previous works. Our results extend to a larger class of non-cooperative models.
Source arXiv, 1307.1651
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