title: Solution of the Dynamics of Liquids in the Large-Dimensional Limit.
abstract: We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions d. The derivation is long but straightforward: a dynamic virial expansion for which only the first two terms survive, followed by a change to generalized spherical coordinates in the dynamic variables leading to saddle-point evaluation of integrals for large d. The problem is, thus, mapped onto a one-dimensional diffusion in a perturbed harmonic potential with colored noise. At high density, an ergodicity-breaking glass transition is found. In this regime, our results agree with thermodynamics, consistently with the general random first order transition scenario. The glass transition density is higher than the best known lower bound for hard sphere packings in large d. Because our calculation is, if not rigorous, elementary, an improvement in the bound for sphere packings in large dimensions is at hand.
authors.affiliation: LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, Paris 75005, France.
authors.forename: Thibaud
authors.initials: T
authors.lastname: Maimbourg
authors.affiliation: LPS, École Normale Supérieure, UMR 8550 CNRS, 24 Rue Lhomond, Paris 75005, France.
authors.forename: Jorge
authors.initials: J
authors.lastname: Kurchan
authors.affiliation: LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, Paris 75005, France.
authors.forename: Francesco
authors.initials: F
authors.lastname: Zamponi