A theoretical framework for calculations of the structural relaxation time on the basis of the free energy landscape theory

On the basis of the free energy landscape theory, we develop a framework to calculate the structural relaxation time in supercooled liquids and glasses. By the framework, the relaxation time is obtained by an escaping time from a basin in a given free energy surface. In order to demonstrate its usefulness, we apply the framework to monodisperse hard-sphere glass systems. Then we show that the relaxation time increases drastically with the density. Additionally, we discuss an explicit picture of the cooperatively rearranging region by analyzing the spatial distribution of an activation free energy of one particle.