Dimensional study of the dynamical arrest in a random Lorentz gas
arXiv:1409.0688 · doi:10.1103/PhysRevE.91.042313
Abstract
The random Lorentz gas is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions d=2-6. Comparing the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with . In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.
9 pages, 6 figures
References in corpus (15)
- Anomalous transport in the crowded world of biological cells
- Fractal free energy landscapes in structural glasses
- Continuum Percolation Thresholds in Two Dimensions
- Hopping and the Stokes-Einstein relation breakdown in simple glass formers
- Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
- Cooperativity Beyond Caging: Generalized Mode Coupling Theory
- Dynamic Glass Transition in Two Dimensions
- Glass transition of hard spheres in high dimensions
- Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
- Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
- Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers
- Rounding of the localization transition in model porous media
- Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory
- Dynamic arrest in model porous media -- intermediate scattering functions
- On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition