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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 | | 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 $Dsim au^{-xi}$ 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 | | Services: | Forum | Review | PDF | Favorites | |
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