期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 52, 期 14, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ab099d
关键词
disordered systems; out-of-equilibrium dynamics; mean field; rheology; metastable glassy states
资金
- European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme [723955]
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.
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