Relaxation dynamics in the energy landscape of glass-forming liquids

Abstract

We numerically study the relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field p-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmonic value at low temperatures. We demonstrate that this apparent evolution is controlled by a temperature-dependent population of localised excitations. Our work unifies several recent lines of studies aiming at a detailed characterization of the complex potential energy landscape of glass-formers.

Gradient descent dynamics and the jamming transition in infinite dimensions

“…For a study of the GD dynamics in many-body (MB) soft harmonic particle systems in varying d we refer to Refs. [14][15][16][17][18][19]. Because finite-dimensional MB systems converge quite slowly to the asymptotic d → ∞ limit [44][45][46][47], here we focus on the simpler Random Lorentz Gas (RLG) [35,36], which is a single particle tracer with d degrees of freedom embedded in a sea of random obstacles.…”

“…At low density, the GD dynamics converges exponentially to a floppy, zero-energy state in which particle overlaps are fully eliminated (unjammed phase). At high density instead, the GD dynamics closely resembles that of mean field spin glasses [16,19], i.e. it displays persistent aging and never reaches a local minimum, while particle overlaps persist at long times, leading to a finite energy (jammed phase).…”

“…For infinitedimensional particle systems, the GD dynamics in the jammed phase is expected to display a non-trivial aging dynamics, belonging to the same universality class of the mixed p-spin model [2]. The energy should then decay as a power-law and correlation functions should age indefinitely; numerical evidence for this has been given in [16,19]. In finite dimensions, the MSD with respect to the initial condition, i.e.…”

“…In finite dimensions, the MSD with respect to the initial condition, i.e. ∆ r (t), reaches a finite plateau [19], which however diverges when d → ∞. Indeed, because in the d → ∞ limit the dynamics becomes a single particle one, the only way to accomodate infinitely persistent aging is for ∆ r (t) to keep growing with t. Because the asymptotic dynamics in this regime is extremely difficult to describe [2], we do not consider the jammed phase here.…”

“…an assembly of finite-range interacting soft repulsive particles [13]. Such a system displays a jamming transition, which is a sharp dynamical phase transition separating two distinct dynamical regimes [14][15][16][17][18][19]. At low density, the GD dynamics converges exponentially to a floppy, zero-energy state in which particle overlaps are fully eliminated (unjammed phase).…”