Chapter 7 - Time-dependent Correlation and Response Functions

Abstract

This chapter deals with the general formalism of time-correlation functions and with linear response theory. It begins by discussing the general properties of time-correlation functions. The discussion is then restricted to systems of particles for which the interaction potential is continuous. The velocity autocorrelation function and self-diffusion are illustrated next. The example of the autocorrelation function of the velocity u =p/m of a tagged particle moving through a fluid is used to demonstrate the concept. The Enskog method is applied. Brownian motion and the generalized Langevin equation are then detailed. The section describes a different approach that is based on the stochastic theory used by Langevin to describe the Brownian motion of a large and massive particle in a bath of particles that are much smaller and lighter than itself. Correlations in space and time are described next. Inelastic neutron scattering, the linear response theory, and applications of the linear-response formalism are discussed as well.