Linear Response and Equilibrium Dynamics

E. Heiner

Abraham Nitzan

Abstract This chapter introduces linear response theory, a general way to describe non-equilibrium system in the vicinity of equilibrium. (1) Classical static and dynamic linear response theory. (2) Quantum static and dynamic linear response theory. (3) Causality and the Kramers–Kronig relations (4) Examples: Mobility, conductivity and diffusion. (5) Thermal noise.

Makoto Ohya

Mathias Frisch

No¨elle Pottier

Abstract Linear response theory is a general formalism applicable to any physical system slightly departing from equilibrium. It allows us to express the linear response functions and the generalized susceptibilities in terms of the equilibrium correlation functions of the relevant dynamical variables. For instance, in the case of the response to an applied external field, one of the two relevant dynamical variables represents the physical quantity conjugate to the field whereas the other represents the physical quantity whose out-of-equilibrium average is measured. The computation of the linear response functions relies on a first-order perturbation expansion of the density operator (or of the phase space distribution function) of the system coupled to the field. The expressions thus obtained constitute the Kubo formulas of linear response theory.

A. K. Rajagopal, S. Teitler

The near-equilibrium nature of dynamic linear response when a system is acted upon by an external force is clarified by using the linearity condition to identify a limited class of near-equilibrium density matrices that characterize the response. The analysis incorporates a distinction between undriven and driven time dependences. Irreversibility is introduced in a traditional way by means of a nonunitary component in the evolution of the undriven dynamics.