Dynamic Response

Abstract

In order to study the intrinsic properties of complex fluids and disordered solids in nonequilibrium situations, a general formulation is needed to describe the dynamic response of a system subjected to an external force field. We shall see in this chapter how the linear response theory relates the nonequilibrium properties of a system directly to fluctuations in equilibrium and, thus, has almost the same validity as equilibrium statistical mechanics. Three commonly used methods of analyzing the nonequilibrium properties of the system are response, relaxation, and susceptibility. Response measures the time evolution of the system under the influence of a time-independent force. Relaxation studies the time-dependent decay after a constant force is removed. Susceptibility investigates the frequency-dependent response to an oscillatory force. We shall see that these properties are not independent of each others. The linear response theory will be used to establish the relationships between the three intrinsic properties of materials. The master equation is fundamental in the study of nonequilibrium stochastic processes, and we shall see it often in the succeeding chapters as a good starting point for analyzing and interpreting cooperative and disordered systems that may be complex fluids, solids, or interfaces.