Random solutions from a regular density functional Hamiltonian: a static and dynamical theory for the structural glass transition

As simple model density functional Hamiltonian is shown to lead to a consistent static and dynamical theory of the structural glass transition where glassy metastable free-energy states play a key role. The crucial concept introduced is a probabilistic order parameter description that results when multiple solutions of the density functional theory are considered where each solution is given a canonical weight. The theory suggests that there are two distinct transition temperatures (or densities). At the higher transition temperature an extensive number of well defined global metastable states appear for the first time. At the lower transition temperature the number of relevant glassy metastable states becomes non-extensive.