Frequency-Dependent Response near the Glass Transition: A Theoretical Model

TL;DR

This paper introduces a theoretical model for the glass transition using a Langevin equation in a temperature-dependent landscape, revealing how system response varies with frequency near the transition.

Contribution

It presents a novel dynamical model linking frequency-dependent response to the glass transition through a piecewise parabolic free energy landscape.

Findings

Identifies a zero-curvature point as the glass transition

Shows a connection between high and low frequency responses

Provides a theoretical framework for glass transition dynamics

Abstract

We propose a simple dynamical model for a glass transition. The dynamics is described by a Langevin equation in a piecewise parabolic free energy landscape, modulated by a temperature dependent overall curvature. The zero-curvature point marks a transition to a phase with broken ergodicity which we identify as the glass transition. Our analysis shows a connection between the high and low frequency response of systems approaching this transition.