Brownian dynamics: From glassy to trivial

Abstract

We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the first, standard, dynamical rules lead to glassy behavior, the other one leads to a simple exponential relaxation towards equilibrium. This finding questions the intrinsic link that exists between the underlying, thermodynamical, energy landscape, and the dynamical rules with which this landscape is explored by the system. Our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.The microscopic phenomena driving the dynamical arrest in supercooled liquids and in glasses are still controversial. One line of thought, which originates in the work of Adam and Gibbs, pictures a glass-forming liquid as a system whose energy landscape complexity accounts for the slowing down of its dynamics. The original Adam-Gibbs [1] theory relates viscosity -the momentum transport coefficient-to configurational entropy. The more recent scenario due to Kirkpatrick, Thirumalai, and Wolynes [2] is based on the study of the metastable configurations of the system and on the concept of nucleating entropic droplets. This is the Random-First-Order Theory (RFOT) scenario. The idea is that metastability arises from the many valleys of the energy landscape the system can be trapped in. The RFOT scenario gives a large set of quantitative predictions including non-mean field particle models [4]. These aspects of the physics of glasses were reviewed by Debenedetti and Stillinger [5] and more recently by Biroli and Bouchaud [6].In another line of thought, no complex energy landscape needs to be invoked, and dynamically induced metastability alone is held responsible for the dynamics slowing down. This is a phenomenological approach in which at a coarse-grained scale local patches of activity are the only ingredients of the dynamics. This has led to the development of kinetically-constrained models (KCM) (see [7] for a review), which have the advantage of lending themselves with greater ease than molecular models to both numerical experiments and analytical treatment. The hallmark of the corresponding lattice models is the absence of any structure in the energy landscape (the equilibrium distribution is that of independent degrees of freedom). These somewhat simplistic descriptions are not directly built from the microscopics, and it is often argued that their glassy-like properties, like the existence of dynamical heterogeneities, are almost tautological, but recent works [8] have tried to bridge the gap from the microscopics to dynamic facilitation.A central concept in both approaches is that of metastability. A metastable state can be viewed as an eigenstate of the evolution operator with a nonzero but small relaxation rate. The existe...

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Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

“…This section is intended to provide a brief overview of theoretical approaches to jammed structures for explaining the relevance of stochastic DFT [44][45][46][47][48][49][50][51][52][53][54][55][56] to the degradation of hyperuniformity.…”

“…To this end, we formulate an analytical form of the non-vanishing zero-wavevector structure factor that satisfies eqn (2) under the condition of eqn (7). A key ingredient of our formulation is the strongcoupling approximation of stochastic density functional theory (DFT) [44][45][46][47][48][49][50][51][52][53][54][55][56] which can consider intermittent fluctuations while fixing the density field at a given distribution of dense packings near and at jamming.…”