Is there a fractional breakdown of the Stokes-Einstein relation in kinetically constrained models at low temperature?
Identifieur interne : 000008 ( Main/Exploration ); précédent : 000007; suivant : 000009Is there a fractional breakdown of the Stokes-Einstein relation in kinetically constrained models at low temperature?
Auteurs : O. Blondel [France] ; C. Toninelli [France]Source :
- EPL [ 0295-5075 ] ; 2014-07-23.
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 a fractional Stokes-Einstein relation 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.
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DOI: 10.1209/0295-5075/107/26005
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Blondel</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>LPMA, CNRS UMR 7599, Université Paris VI-VII, Bâtiment Sophie Germain - 5 rue Thomas Mann, 75205 Paris CEDEX 13</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement></placeName></affiliation></author><author><name sortKey="Toninelli, C" sort="Toninelli, C" uniqKey="Toninelli C" first="C." last="Toninelli">C. 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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 a fractional Stokes-Einstein relation 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.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Blondel, O" sort="Blondel, O" uniqKey="Blondel O" first="O." last="Blondel">O. Blondel</name></region><name sortKey="Toninelli, C" sort="Toninelli, C" uniqKey="Toninelli C" first="C." last="Toninelli">C. Toninelli</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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