Interplay between percolation and glassiness in the random Lorentz gas

Abstract

The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media. It also models the dynamics of a tracer in a glassy system. These two perspectives, however, are fundamentally inconsistent. Arrest in the former is related to percolation, and hence continuous, while glass-like arrest is discontinuous. In order to clarify the interplay between percolation and glassiness in the RLG, we consider its exact solution in the infinite-dimensional $d\to \infty$ limit, as well as numerics in $d=2\dots 20$. We find that the mean field solutions of the RLG and glasses fall in the same universality class, and that instantonic corrections related to rare cage escapes destroy the glass transition in finite dimensions. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of hopping in structural glasses.

arXiv comment10 pages, 5 figures

References in corpus (29)

• Theoretical perspective on the glass transition and amorphous materials
• Anomalous transport in the crowded world of biological cells
• Mean field theory of hard sphere glasses and jamming
• A fast Monte Carlo algorithm for site or bond percolation
• The role of local structure in dynamical arrest
• Continuum Percolation Thresholds in Two Dimensions
• Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids
• Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation
• Jamming versus Glass Transitions
• A theory of amorphous packings of binary mixtures of hard spheres
• The simplest model of jamming
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Thermodynamics of binary mixture glasses
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Single-particle and collective slow dynamics of colloids in porous confinement
• Slow dynamics in random media: Crossover from glass to localization transition
• Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
• Activated events in glasses: the structure of entropic droplets
• Anomalous Low-Field Classical Magnetoresistance in Two Dimensions
• Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers
• From discrete to continuous percolation in dimensions 3 to 7
• Quantitative approximation schemes for glasses
• Glassy dynamics of partially pinned fluids: an alternative mode-coupling approach
• Finite-dimensional vestige of spinodal criticality above the dynamical glass transition
• Dimensional study of the dynamical arrest in a random Lorentz gas
• Gaussian density fluctuations, mode coupling theory, and all that
• Void distributions reveal structural link between jammed packings and protein cores
• Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices
• Note: A replica liquid theory of binary mixtures

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• Mean-field caging in a random Lorentz gas
• Correlation of plastic events with local structure in jammed packings across spatial dimensions
• The dimensional evolution of structure and dynamics in hard sphere liquids
• Equilibrium Fluctuations in Mean-field Disordered Models
• Jamming, relaxation, and memory in a structureless glass former
• High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas
• Jammed solids with pins: Thresholds, Force networks and Elasticity
• Percolation thresholds on high dimensional $D_n$ and dense packing lattices
• Dynamics and fluctuations of minimally-structured glass formers
• Not-so-glass-like Caging and Fluctuations of an Active Matter Model
• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"
• The geometry of jamming algorithms in the random Lorentz gas
• Glass-like Caging with Random Planes
• Rare Trajectories in a Prototypical Mean-field Disordered Model: Insights into Landscape and Instantons
• Gradient descent dynamics and the jamming transition in infinite dimensions