Long-range correlations in glasses and glassy fluids

We argue that the existence of a non-decaying part of the self-intermediate scattering function implies a small wave-vector divergence of a four-point structure factor defined in terms of the microscopic self-intermediate scattering function. This divergence indicates long-range correlations of density fluctuations in direct space. We show that a signature of the divergence and the long-range correlations can be observed in computer simulations of glasses. Interestingly, remnants of this divergence can be easily observed in computer simulations of supercooled fluids. They manifest themselves as transient dynamic correlations with a very large correlation length; much larger than the correlation length characterizing the size of dynamic heterogeneities.