Beyond the mode-coupling theory: a perturbative diagrammatic approach

We analyze corrections to the mode-coupling theory of the glass transition, focusing on the self-consistent equation for the non-ergodicity parameter. We use a diagrammatic formulation of the dynamics of interacting Brownian particles\footnote{G. Szamel, J. Chem. Phys. 127, 084515 (2007)}. Our approach builds upon an earlier identification of a divergent contribution to a four-point correlation function\footnote{G. Szamel, Phys. Rev. Lett. 101, 205701 (2008)}. We find that diagrams similar to those generating the divergence of the four-point function lead to divergent corrections to the mode-coupling theory's prediction for the long time limit of the irreducible memory function. We propose and investigate a new equation for the non-ergodicity parameter that self-consistently includes the diagrams leading to the divergent corrections.