Correlations, response, and dissipation

Abstract

This chapter studies how systems wiggle, and how they respond and dissipate energy when kicked. The wiggling fluctuations are described using correlation functions, the yielding and dissipation are described using susceptibilities. The intricate relations between these quantities are explored using the Onsager regression hypothesis, fluctuation--response and fluctuation--dissipation theorems, and the Kramers--Krönig relation derived from causality (the response cannot precede the kick). The powerful tools of linear response theory described here are basic tools in our exploration of materials with scattering of sound, light, X-rays, and neutrons, and have become our primary description of the behavior of materials. Exercises describe applications to noise in nanojunctions, humans on subways, magnetic spins, molecular dynamics and Ising models, liquids and magnets, materials at critical points, and fluctuations in the early Universe.