Microscopic theory for hopping transport in glass-forming liquids

Under the assumption that structural relaxation is dominated by the decay of clusters of particles, we develop a microscopic theory for transport in a strongly supercooled liquid. By introducing a local order parameter that describes the geometry of particle aggregates in addition to the number density and momentum density, we obtain an expression for the effective longitudinal viscosity in which a hopping tem emerges nonperturbatively. We find that the hopping kernel of the present work arises from couplings to bilinear density-momentum modes in agreement with previous mode-coupling treatments. However, the magnitude of the hopping kernel is suppressed through a wave vector cutoff instead of the previously suggested initial time cutoff