The glass transition singularity

The mode coupling equations which were derived before within a kinetic theory approach for a dynamical description of simple classical liquids, are truncated such that leading and next to leading order contributions to the relaxation kernels caused by density fluctuations are kept. As a result closed non linear equations for density and current fluctuations are obtained which extend the equations used by Bengtzelius et al. for the discussion of the liquid glass transition. Considering the correlations as functions of vertex parameters and frequencies, singularities for zero frequency and certain subsets in parameter space are identified. For a schematic model the correlation functions near the singularities can be discussed in terms of various scaling laws. If a temperature variation drives the system close to the singularity the latter cause strong anomalies of the low frequency dynamics. The anomalies are discussed and shown to correlate qualitatively with the experimentally known ones for glass transitions.