Dynamical Response Theory for Driven-Dissipative Quantum Systems

TL;DR

This paper develops a response theory for driven-dissipative quantum systems, deriving explicit formulas for response functions, introducing maximal harmonic response, and analyzing dynamical phase transitions.

Contribution

It provides a new framework for understanding linear response in non-equilibrium open quantum systems, including explicit calculations and phase transition analysis.

Findings

Explicit response functions for specific quantum channels

Introduction of maximal harmonic response concept

Identification of spectral peaks at phase transitions

Abstract

We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and dissipative perturbations are considered besides the Hamiltonian ones. We derive explicit expressions for the linear dynamical response functions for generalized dephasing channels and for Davies thermalizing generators. We introduce the notion of maximal harmonic response and compute it exactly for a single qubit channel. Finally, we analyze linear response near dynamical phase transitions in quasi-free open quantum systems. It is found that the effect of the dynamical phase transition shows up in a peak at the edge of the spectrum in the imaginary part of the dynamical response function.