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Abstract
We report the results of a large scale computer simulation of a binary supercooled
Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared
displacement of a tagged particle for different temperatures fall onto a master curve
when they are plotted versus rescaled time \(tD(T)\), where \(D(T)\) is the diffusion
constant. The time range for which these curves follow the master curve is identified
with the \(\alpha\)-relaxation regime of mode-coupling theory (MCT). This master curve
is fitted well by a functional form suggested by MCT. In accordance with idealized
MCT, \(D(T)\) shows a power-law behavior at low temperatures. The critical temperature
of this power-law is the same for both types of particle and also the critical exponents
are very similar. However, contrary to a prediction of MCT, these exponents are not
equal to the ones determined previously for the divergence of the relaxation times
of the intermediate scattering function [Phys. Rev. Lett. {\bf 73}, 1376 (1994)].
At low temperatures the van Hove correlation function (self as well as distinct part)
shows hardly any sign of relaxation in a time interval that extends over about three
decades in time. This time interval can be interpreted as the \(\beta\)-relaxation regime
of MCT. From the investigation of these correlation functions we conclude that hopping
processes are not important on the time scale of the \(\beta\)-relaxation for this system
and for the temperature range investigated. We test whether the factorization property
predicted by MCT holds and find that this is indeed the case for all correlation functions
investigated. The distance dependence of the critical amplitudes are in qualitative
accordance with the ones predicted by MCT for some other mixtures. The non-gaussian
parameter for the self part of the van