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

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.