Mode-coupling theory for the shear viscosity in supercooled liquids

The mode-coupling theory for the shear viscosity for supercooled liquids is generalized so that, in addition to density-fluctuation pairs, current-fluctuation pairs are taken into account. As a consequence the wave-vector and frequency-dependent shear viscosity reproduces in addition to the structural relaxation anomalies the known hydrodynamic long-time tail. In the supercooled state there appears a temperature-sensitive crossover from structural relaxation to the hydrodynamic long-time anomaly.