Response Theory and Response Functions

Ming-Bao Yu

Stefan Floerchinger

Response theory describes the reaction of observales to perturbations in external fields. We review this formalism for quantum fiels in isolation that have unitary time evolution. An emphasis is put on consequences of causality and the resulting spectral representations for linear and nonlinear response functions, on functional techniques and generating functionals, including the description of the initial state, the evolution, and measurements. We review consequences of time reversal symmetry and relations for the statistics of work, and discuss a large class of quantum correlation functions, and their relation to response functions through fluctuation-dissipation relations. Consequences of conservation laws and gauge symmetries are mentioned briefly.

Gabor J. Kalman, J. M. Rommel

While the theory of linear response functions in many body theory has developed into a substantial lore over the past decades, rather little is known about the properties and behavior of higher order (quadratic, etc.) response functions of many body systems. In this poster we first review essential elements of quadratic response theory such as the quadratic fluctuation dissipation theorems and sum rules for the quadratic density response function. Next we show how the correlational local field G(k,ω) in the linear response is fundamentally linked to the quadratic response function which opens a way to a non-perturbational analysis of the former. We proceed to present the results of the explicit calculation of the quadratic density response of 2D and 3D electron gas. Both, real and imaginary part of the latter reveal an extremely rich behavior. Of particular interest is the comparison between the two- and the three-dimensional case.

Mathias Frisch