Solution of the Dynamics of Liquids in the Large-Dimensional Limit

Physical Review Letters
Thibaud MaimbourgFrancesco Zamponi

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.

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Citations

Dec 24, 2017·The Journal of Chemical Physics·Harukuni IkedaAtsushi Ikeda
Dec 9, 2017·Physical Review Letters·Matthieu Wyart, Michael E Cates
Jun 13, 2018·Soft Matter·Beatriz Seoane, Francesco Zamponi
Aug 31, 2019·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Liesbeth M C Janssen
Jul 6, 2019·The Journal of Chemical Physics·Ludovic BerthierFrancesco Zamponi
Jun 28, 2016·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Jeppe C Dyre
Oct 24, 2019·Physical Review. E·Ada Altieri, Francesco Zamponi
Jan 18, 2020·Physical Review Letters·Thibaut Arnoulx de PireyFrédéric van Wijland
May 3, 2020·The Journal of Chemical Physics·Alessandro ManacordaFrancesco Zamponi
Feb 6, 2017·Physical Review Letters·Pierfrancesco Urbani, Francesco Zamponi
Jun 17, 2018·The Journal of Chemical Physics·Benoit CharbonneauGrzegorz Szamel
Nov 18, 2018·Physical Review Letters·Ada AltieriFrancesco Zamponi
Feb 20, 2019·Physical Review. E·Camille ScallietFrancesco Zamponi
Sep 1, 2019·The Journal of Chemical Physics·Marco Baity-Jesi, David R Reichman
Oct 28, 2017·Physical Review Letters·Grzegorz Szamel
Feb 13, 2016·Physical Review. E·Matthieu Mangeat, Francesco Zamponi
Jun 10, 2018·The Journal of Chemical Physics·Edan Lerner, Eran Bouchbinder
Oct 21, 2020·Physical Review. E·Gerhard JungThomas Franosch
Dec 10, 2020·The Journal of Chemical Physics·Chengjie Luo, Liesbeth M C Janssen
Dec 10, 2020·The Journal of Chemical Physics·Chengjie Luo, Liesbeth M C Janssen
Mar 20, 2021·Physical Review. E·Harukuni IkedaAtushi Ikeda
May 2, 2021·Proceedings of the National Academy of Sciences of the United States of America·Peter K MorseM Lisa Manning
Jun 8, 2021·The Journal of Physical Chemistry. B·Giulio BiroliFrancesco Zamponi

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