Relaxation dynamics in the energy landscape of glass-forming liquids

TL;DR

This study investigates the relaxation dynamics of glass-forming liquids across different models, revealing distinct behaviors in mean-field and finite-dimensional systems and highlighting the role of localized excitations.

Contribution

It provides a unified analysis of relaxation behaviors in glass-formers, contrasting mean-field and finite-dimensional models, and emphasizes the influence of localized excitations on dynamics.

Findings

Mean-field models show a transition from power-law to exponential relaxation.

Finite-dimensional systems exhibit persistent algebraic relaxation with temperature-dependent exponents.

Localized glassy excitations control the relaxation crossover.

Abstract

We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial 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 glassy excitations. Our work unifies several recent lines of studies aiming at a detailed characterisation of the complex potential energy landscape of glass-formers, and challenges both mean-field and real space descriptions of glasses.