Ergodicity-breaking transition and high-frequency response in a simple free-energy landscape

Abstract
We present a simple dynamical model 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. The frequency-dependent response near this transition is reminiscent of observations near the glass transition.