Comments on the mode coupling theory for structural relaxation

In condensed matter the coupling of fluctuating forces to the infinite set of density fluctuation pairs leads to non-Markovian equations for the time evolution. Treating the dynamics of the density pairs with a factorization approximation yields closed equations of motion which provide a mathematically well-defined treatment of the cage effect for particle motion in liquids. The equations imply a bifurcation singularity connected with the appearance of a spontaneous arrest of the particle positions in disordered arrays. The evolution of structural relaxation on cooling or compression of liquids is obtained when the temperature or density approach critical values, which characterize the singularity. Von Schweidler's law is obtained as a generic reason for α-relaxation stretching. There appears a dynamical window where structural relaxation is described by a universal law, which deals with two time fractals. The relation of the mode coupling theory with Mountain's theory of structural relaxation is discussed and the interplay of relaxations and oscillations in supercooled liquids is demonstrated.