Abstract
Whereas Chapter 8 was concerned with semi-phenomenological theories of time correlation functions, this chapter provides a systematic theoretical framework for the calculation of these correlation functions, starting from the exact Liouville equation, and using a projection operator approach; this leads to microscopic expressions for a hierarchy of memory functions. The resulting formalism is applied to the calculation of self (single-particle) correlation functions, as well as those corresponding to transverse and longitudinal collective modes, including the spectrum of density fluctuations measured by inelastic neutron or X-ray scattering. It is shown that mode coupling theory can account for the long-time decay of the velocity autocorrelation function and for the structural arrest associated with the kinetic glass transition.
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