Some consequences of the α/β bifurcation of relaxations in supercooled liquids

Because it is a doubly projected quantity and is related to correlation functions of gradients of the intermolecular potential, the normalized second memory function corresponding to the relaxation of a dynamical quantity A(t) is taken to be a relaxation function dependent only upon collective modes and independent of the specific nature of the variable A(t). From this assumption alone the relaxation properties of many variables A(t) can be obtained and a rationale for the generalized Stokes-Einstein relation can be given. Further, by assuming that this memory function is biexponential, many of the properties characteristics of systems which exhibit bifurcation of their slow relaxations into α and 'slow β' processes can be obtained.