Response functions after a quantum quench

TL;DR

This paper develops a method to extract full dynamical response functions, including linear responses, from quantum systems after a quench, extending previous work focused only on symmetrized correlations, and demonstrates light-cone effects in these responses.

Contribution

It introduces a new prescription to obtain complete dynamical response functions from static boundary theories after a quantum quench, broadening the scope of previous methods.

Findings

Method allows retrieval of full dynamical response functions.

Demonstrates emergence of light-cone effects in response functions.

Extends previous approaches focused solely on correlation functions.

Abstract

The response of physical systems to external perturbations can be used to probe both their equilibrium and non-equilibrium dynamics. While response and correlation functions are related in equilibrium by fluctuation-dissipation theorems, out of equilibrium they provide complementary information on the dynamics. In the past years, a method has been devised to map the quantum dynamics of an isolated extended system after a quench onto a static theory with boundaries in imaginary time; up to now, however, the focus was entirely on symmetrized correlation functions. Here we provide a prescription which, in principle, allows one to retrieve the whole set of relevant dynamical quantities characterizing the evolution, including linear response functions. We illustrate this construction with some relevant examples, showing in the process the emergence of light-cone effects similar to those observed in correlation functions.