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Tracer diffusion at low temperature in kinetically constrained models | | Oriane Blondel
; | | Date: |
27 Jun 2013 | | Abstract: | We describe the motion of a tracer in an environment given by a kinetically
constrained spin model (KCSM) at equilibrium. We check convergence of its
trajectory properly rescaled to a Brownian motion and positivity of the
diffusion coefficient $D$ as soon as the spectral gap of the environment is
positive (which coincides with the ergodicity region under general conditions).
Then we study the asymptotic behaviour of $D$ when the density $1-q$ of the
environment goes to 1 in two classes of KCSM. For non-cooperative models, the
diffusion coefficient $D$ scales like a power of $q$, with an exponent that we
compute explicitly. In the case of the Fredrickson-Andersen one-spin
facilitated model, this proves a prediction made in
cite{junggarrahanchandler}. For the East model, instead we prove that the
diffusion coefficient is comparable to the spectral gap, which goes to zero
faster than any power of $q$. This result contradicts the prediction of
physicists (cite{junggarrahanchandler}), based on numerical simulations, that
suggested $Dsim gap^xi$ with $xi<1$. | | Source: | arXiv, 1306.6500 | | Services: | Forum | Review | PDF | Favorites | |
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