Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation

Abstract

The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory, an excellent matching of both the critical density and exponents is obtained. Upon exploiting a dynamic scaling Ansatz employing two divergent length scales we find data collapse for the mean-square displacements and identify the leading-order corrections to scaling. The non-Gaussian parameter is predicted to diverge at the transition.

extended introduction, minor changes in Fig. 2b and one reference added

References in corpus (2)

• Direct experimental evidence of a growing length scale accompanying the glass transition
• Subdiffusion and dynamical heterogeneities in a lattice glass model

Cited by in corpus (75)

• Anomalous transport in the crowded world of biological cells
• Anomalous, non-Gaussian tracer diffusion in heterogeneously crowded environments
• Anomalous dynamics of intruders in a crowded environment of mobile obstacles
• Multiple Glasses in Asymmetric Binary Hard Spheres
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Non-universal tracer diffusion in crowded media of non-inert obstacles
• A Double-Transition Scenario for Anomalous Diffusion in Glass-Forming Mixtures
• Development of anomalous diffusion among crowding proteins
• 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
• Colloids in light fields: particle dynamics in random and periodic energy landscapes
• Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model
• Diffusion, subdiffusion and localisation of active colloids in random post lattices
• The Localization Transition of the Two-Dimensional Lorentz Model
• Slow dynamics in random media: Crossover from glass to localization transition
• Critical dynamics of ballistic and Brownian particles in a heterogeneous environment
• Localization dynamics of fluids in random confinement
• Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
• Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy
• Mode-coupling theory of the glass transition for confined fluids
• Splitting of the universality class of anomalous transport in crowded media
• Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
• Anomalous transport resolved in space and time by fluorescence correlation spectroscopy
• Rounding of the localization transition in model porous media
• Anomalous diffusion in random dynamical systems
• Brownian particles on rough substrates: Relation between the intermediate subdiffusion and the asymptotic long-time diffusion
• Persistent memory for a Brownian walker in a random array of obstacles
• Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory
• Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium
• Ideal circle microswimmers in crowded media
• Enhanced Diffusion of a Needle in a Planar Course of Point Obstacles
• Impact of random obstacles on the dynamics of a dense colloidal fluid
• Dynamic arrest of colloids in porous environments: disentangling crowding and confinement
• Statistical mechanics of homogeneous partly pinned fluid systems
• Mobile particles in an immobile environment: Molecular Dynamics simulation of a binary Yukawa mixture
• Interplay between percolation and glassiness in the random Lorentz gas
• Molecular finite-size effects in stochastic models of equilibrium chemical systems
• Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions
• Dimensional study of the dynamical arrest in a random Lorentz gas
• Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues
• Anomalous magneto-transport in disordered structures: classical edge-state percolation
• Local dynamical heterogeneity in glass formers
• Mean-field caging in a random Lorentz gas
• Anomalous transport of a tracer on percolating clusters
• Random motion of a circle microswimmer in a random environment
• Dynamic arrest in model porous media -- intermediate scattering functions
• Superdiffusion dominates intracellular particle motion in the supercrowded space of pathogenic Acanthamoeba castellanii
• Space-resolved dynamics of a tracer in a disordered solid
• Dynamic heterogeneities and non-Gaussian behavior in two-dimensional randomly confined colloidal fluids
• Nonmonotonous classical magneto-conductivity of a two-dimensional electron gas in a disordered array of obstacles
• Crowding of interacting fluid particles in porous media through molecular dynamics: breakdown of universality for soft interactions
• Nonergodic subdiffusion from transient interactions with heterogeneous partners
• Percolation through Voids around Randomly Oriented Platonic Solids
• Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature
• Colloids Exposed to Random Potential Energy Landscapes: from Particle Number Density to Particle-Potential and Particle-Particle Interactions
• Memory effects in colloidal motion under confinement and driving
• Anomalous transport in the soft-sphere Lorentz model
• Localization phenomena in models of ion-conducting glass formers
• Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering
• High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas
• Hydrogen diffusion in garnet: insights from atomistic simulations
• Universal Particle Kinetic Distribution in Crowded Environments
• Diffusion in jammed particle packs
• Jamming vs. Caging in Three Dimensional Jamming Percolation
• Continuous demixing transition of binary liquids: finite-size scaling from the analysis of sub-systems
• Brownian Yet Non-Gaussian Diffusion of a Light Particle in Heavy Gas: Lorentz Gas Based Analysis
• Horizons and free path distributions in quasiperiodic Lorentz gases
• First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results
• Not-so-glass-like Caging and Fluctuations of an Active Matter Model
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Competing Relaxation Channels in Continuously Polydisperse Fluids: A Mode-Coupling Study
• Non-scaling displacement distributions as may be seen in fluorescence correlation spectroscopy
• Percolation through Voids around Toroidal Inclusions
• Scaling study of diffusion in dynamic crowded spaces
• Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach