Revisiting the single-saddle model for the $\beta$-relaxation of supercooled liquids

TL;DR

This paper revisits a simple theoretical model for the initial beta-relaxation in supercooled liquids, extending it to include density correlations and comparing predictions with simulations, highlighting its strengths and limitations.

Contribution

The work extends the single-saddle model to include density correlations and compares its predictions with simulations, revealing its quantitative accuracy in early beta-regime and limitations for structural relaxation.

Findings

Model accurately predicts early beta-relaxation dynamics.

Quantitative agreement with simulations in the initial beta-regime.

Inherent harmonic approximation limits predictions for long-time structural relaxation.

Abstract

The dynamics of glass-forming liquids display several outstanding features, such as two-step relaxation and dynamic heterogeneities, which are difficult to predict quantitatively from first principles. In this work, we revisit a simple theoretical model of the $\beta$-relaxation, i.e., the first step of the relaxation dynamics. The model, first introduced by Cavagna et al., describes the dynamics of the system in the neighborhood of a saddle point of the potential energy surface. We extend the model to account for density-density correlation functions and for the 4-point dynamic susceptibility. We obtain analytical results for a simple schematic model, making contact with related results for p-spin models and with the predictions of inhomogeneous mode-coupling theory. Building on recent computational advances, we also explicitly compare the model predictions against overdamped Langevin dynamics simulations of a glass-forming liquid close to the mode-coupling crossover. The agreement is quantitative at the level of single-particle dynamic properties only up to the early $\beta$-regime. Due to its inherent harmonic approximation, however, the model is unable to predict the dynamics on the time scale relevant for structural relaxation. Nonetheless, our analysis suggests that the agreement with the simulations may be largely improved if the modes' spatial localization is properly taken into account.