## Is there a breakdown of the Stokes-Einstein relation in Kinetically Constrained Models at low temperature?    [PDF]

Oriane Blondel, Cristina Toninelli
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 $D\sim\tau^{-1}$ at leading order for very large time-scales. Our results still suggest a violation but weaker, $D\tau\sim 1/q^\alpha$, 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 $D\sim\tau^{-1}$ in dimension 2 and higher, confirming previous works. Our results extend to a larger class of non-cooperative models.
View original: http://arxiv.org/abs/1307.1651