Fluctuating hydrodynamics and glass transition theory

Kawasaki's mode-coupling theory is used for deriving and solving non-linear equations of the fluctuating hydrodynamics for a simple fluid. The ergodicity-nonergodicity transition (glass transition) associated with the existence of a zero-frequency pole in the Laplace spectrum of the density correlation function has been discussed. The behaviour of the dynamical viscosity and dynamical moduli in the vicinity of transition has been studied in detail. The physical sense of the glass transition criterion has been considered, and it is compared to the percolation threshold for the overlapping spheres problem.