  We investigate the origin of the breakdown of the Stokes-Einstein relation
(SER) between diffusivity and viscosity in undercooled melts. A binary
Lennard-Jones system, as a model for a metallic melt, is studied by molecular
dynamics. A weak breakdown at high temperatures can be understood from the
collectivization of motion, seen in the isotope effect. The strong breakdown at
lower temperatures is connected to an increase in dynamic heterogeneity. On
relevant timescales some particles diffuse much faster than the average or than
predicted by the SER. The van-Hove self correlation function allows to
unambiguously identify slow particles. Their diffusivity is even less than
predicted by the SER. The time-span of these particles being slow particles,
before their first conversion to be a fast one, is larger than the decay time
of the stress correlation. The contribution of the slow particles to the
viscosity rises rapidly upon cooling. Not only the diffusion but also the
viscosity shows a dynamically heterogeneous scenario. We can define a "slow"
viscosity. The SER is recovered as relation between slow diffusivity and slow
viscosity.
