Chapter 9 - Theories of Time-correlation Functions

Abstract

The chapter addresses the problem of devising a general theoretical scheme for the calculation of time-correlation functions at wavelengths and frequencies on the molecular scale. Memory functions play a key role in the theoretical development and the chapter begins by showing how the memory-function approach can be formalized through the use of the projection-operator methods of Zwanzig and Mori. The calculation of the memory function is a specific problem described as a separate task that can be tackled along two different lines. The first represents a systematic extension of the ideas of generalized hydrodynamics; the second is more microscopic in nature and based on the mode-coupling approach. The projection-operator formalism is discussed first. Self-correlation functions, transverse collective modes, and density fluctuations are described. The appearance of propagating shear waves in dense fluids can be explained in qualitative or even semi-quantitative terms by a simple, viscoelastic model based on a generalization of the hydrodynamic approach. Transverse collective modes show how such a theory can be developed in systematic fashion by use of the projection-operator formalism. The chapter also provides information on mode-coupling theory 1 and the velocity correlation function, and mode-coupling theory 2 and the kinetic glass transition.