Linear Response

A. Kallio, M. Puoskari, Lauri J. Lantto +2 more

Sandip Tiwari

Abstract This chapter focuses on the properties associated with linear response. Reversibility holds in linear transformations. Schrödinger and Maxwell equations are linear, yet the world is irreversible, with time marching forward and dissipation quite ubiquitous. The connections between the quantum and microscopic scale, which are reversible and non-deterministic, to the macroscale, where irreversibility and determinism abounds, arise through interactions where both linear and nonlinear responses can appear. Causality’s implication in linear response is illustrated through a toy example and a quantum-statistical view of response. Linear response theory—using Green’s functions—is applied to develop dispersion relationships and dielectric function. The tie-in between real and imaginary parts is illustrated as one example of the Kramers-Kronig relationship, and the linear response of a damped oscillator and the Lorentz model, together with the oscillating electron model, employed to illustrate the dielectric function implications.

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.

Mathias Frisch

Malin Premaratne, Govind Prasad Agrawal