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Abstract
摘要 |
Many different dynamical processes are entangled around the glass transition, including the mode-coupling theory (MCT) collective slowdown, crystal nucleation, glass-glass nucleation, hopping, facilitation, and dynamical heterogeneity. Here we examine the hopping contribution in a mean-field version of the hard sphere model that excludes all other except for the MCT slowdown. We find that hopping broadens the dynamical transition (which is here thermodynamically well defined), and that the MCT scaling as well as the Stokes-Einstein relation breaks down because of it. Removing hopping leaves the particles in cages that are stable beyond the dynamical transition predicted by thermodynamic theories. The size of the cages thus obtained is calculated theoretically using the replica and the cavity methods, and is in good agreement with full system simulations. In higher spatial dimensions, we find that hopping becomes less relevant, and so we expect the mean-field theories to become asymptotically exact with increasing dimension. We also show that caging and hopping have an intrinsic relation to void percolation. |
