title: Dimensional study of the dynamical arrest in a random Lorentz gas.
abstract: The random Lorentz gas (RLG) 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. Comparison of the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with d. 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.
authors.affiliation: Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.|Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sezione di Roma I, IPFC-CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy.|LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France.
authors.forename: Yuliang
authors.initials: Y
authors.lastname: Jin
authors.affiliation: Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.|Department of Physics, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Patrick
authors.initials: P
authors.lastname: Charbonneau
mesh_terms: D005740:Gases / Q000737:chemistry*; D005898:Glass / Q000737:chemistry*; D057446:Hydrodynamics; D008962:Models, Theoretical; D044367:Phase Transition
chemical_list: D005740:Gases