Correlation Functions, Scattering, and Response

Abstract

In the following, we investigate the dynamical properties of many-particle systems on a microscopic, quantum-mechanical basis. We begin by expressing experimentally relevant quantities such as the inelastic scattering crosssection and the dynamical susceptibility (which describes the response of the system to time-dependent fields) in terms of microscopic entities such as the dynamical correlation functions. To this end the time-evolution operator will be determined perturbatively using the interaction representation. General properties of these correlation functions and their interrelations are then derived using the symmetry properties of the system, causality, and the specific definitions in terms of equilibrium expectation values. Finally, we calculate correlation functions for a few physically relevant models.