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 $\log (D)=-\log (\tau )+O(\log (1/q))$, which implies at leading order $\log (D)/\log (\tau )\sim -1$ for very large time-scales. Our results do not exclude the possibility of SE breakdown, albeit non fractional. Indeed extended numerical simulations by other authors show the occurrence of this violation and our result suggests $D\tau \sim 1/q^{\alpha }$, 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.

6 pages, 2 figures; v2: revised version, to appear in EPL

References in corpus (4)

• Theoretical perspective on the glass transition and amorphous materials
• Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids
• Dynamical Exchanges in Facilitated Models of Supercooled liquids
• Lengthscale dependence of dynamic four-point susceptibilities in glass formers

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• A class of random walks in reversible dynamic environment: antisymmetry and applications to the East model
• Dynamic Heterogeneity in Crossover Spin Facilitated Model of Supercooled Liquid and Fractional Stokes-Einstein Relation
• Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation