Out-of-equilibrium dynamical equations of infinite-dimensional particle systems I. The isotropic case

We consider the Langevin dynamics of a many-body system of interacting particles in d dimensions, in a very general setting suitable to model several out-of-equilibrium situations, such as liquid and glass rheology, active self-propelled particles, and glassy aging dynamics. The pair interaction potential is generic, and can be chosen to model colloids, atomic liquids, and granular materials. In the limit d -> infinity, we show that the dynamics can be exactly reduced to a single one-dimensional effective stochastic equation, with an effective thermal bath described by kernels that have to be determined self-consistently. We present two complementary derivations, via a dynamical cavity method and via a path-integral approach. From the effective stochastic equation, one can compute dynamical observables such as pressure, shear stress, particle mean-square displacement, and the associated response function. As an application of our results, we derive dynamically the 'state-following' equations that describe the response of a glass to quasistatic perturbations, thus bypassing the use of replicas. The article is written in a modular way, that allows the reader to skip the details of the derivations and focus on the physical setting and the main results.


Published in:
Journal Of Physics A-Mathematical And Theoretical, 52, 14, 144002
Year:
Apr 05 2019
Publisher:
Bristol, IOP PUBLISHING LTD
ISSN:
1751-8113
1751-8121
Keywords:
Laboratories:




 Record created 2019-06-18, last modified 2019-08-06


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