Is there a fractional breakdown of the Stokes-Einstein relation in kinetically constrained models at low temperature?

LPMA, CNRS UMR 7599, Université Paris VI-VII, Bâtiment Sophie Germain - 5 rue Thomas Mann, 75205 Paris CEDEX 13, France

Received: 28 February 2014
Accepted: 1 July 2014

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 with . We present rigorous results proving that instead , which implies at leading order 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 , where q is the density of excitations. For FA1f we prove a fractional Stokes-Einstein relation in dimension 1, and in dimension 2 and higher, confirming previous works. Our results extend to a larger class of non-cooperative models.