On linear-response dynamics

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.

Kai Luo, Peter D. T. A. Elliott, Neepa T. Maitra

Recent work [Phys. Rev. Lett. 109, 266404 (2012)] showed that the exact exchange-correlation potential of time-dependent density-functional theory generically displays dynamical step structures. These have a spatially nonlocal and time-nonlocal dependence on the density in real-time dynamics. The steps are missing in the usual approximations, which consequently yield inaccurate dynamics. Yet these same approximations often yield good linear response spectra. Here we investigate whether the steps appear in the linear response regime, when the response is calculated from a real-time dynamics simulation, by examining the exact correlation potential of model two-electron systems at various times. We find there are no step structures in regions where the system response is linear. Step structures appear in the correlation potential only in regions of space where the density response is nonlinear; these regions, having exponentially small density, do not contribute to the observables measured in linear response.

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.

Malin Premaratne, Govind Prasad Agrawal