Correlation functions for glass-forming systems

We present a simple, linear, partial-differential equation for the density-density correlation function in a glass-forming system. The equation is written down on the basis of fundamental and general considerations of linearity, symmetry, stability, thermodynamic irreversibility and consistency with the equation of continuity (i.e. , conservation of matter). The dynamical properties of the solutions show a change in behavior characteristic of the liquid-glass transition as a function of one of the parameters (temperature). The equation can be shown to lead to the simplest mode-coupling theory of glasses and provides a partial justification of this simplest theory. It provides also a method for calculating the space dependence of the correlation functions not available otherwise. The results suggest certain differences in behavior between glassy solids and glass-forming liquids which may be accessible to experiment. A brief discussion is presented of how the method can be applied to other systems such as sandpiles and vortex glasses in type II superconductors.