Relationship Between Theory and Experiment
Biman Bagchi · 2023
Overview From the very beginning, the study of time-dependent statistical mechanics has been intimately connected with experiments so much so that most of the theoretical methods, starting with Einstein’s famous theory of Brownian motion, have been developed in response to experimental results. In experiments, we often subject a system of interest to a small perturbation and measure the resultant change in its properties. The measured properties are called response functions. In equilibrium statistical mechanics, these perturbations are time-independent and the response is given, in the appropriate cases, by quantities such as specific heat, isothermal compressibility, dielectric constant. So, when we want to learn about dynamic response functions of the system and transport properties, we impose time-dependent perturbations, which might be in the form of a beam of neutrons, exciting light, fluctuating electric field, etc. There are also experimental methods that employ an incident radiation and measure absorption or scattering as a function of frequency and wavenumber. In general, it is fair to state that the experiments can be broadly divided into these two categories – time domain and frequency domain. In this chapter, we shall learn about the theoretical analyses and approaches that allow us to build the relationship between theory and experiments. The experimental observables are often related to time correlation functions (TCF), which in turn contain information about the dynamics of the system. For example, infra-red (IR) spectroscopy provides information about orientational TCF, and the Rayleigh-Brillouin spectrum is given by density-density TCF. The present chapter describes these relationships between experimental observables and theoretical counterparts.