Dynamical Response Theory for Driven-Dissipative Quantum Systems

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.

9 pages, 3 figures, comments welcome

References in corpus (8)

• An Open-System Quantum Simulator with Trapped Ions
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
• Quantum response of dephasing open systems
• Geometry, robustness, and emerging unitarity in dissipation-projected dynamics

Cited by in corpus (18)

• Tenfold Way for Quadratic Lindbladians
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• Geometry and response of Lindbladians
• Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
• Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators
• Time-dependent Correlation Functions in Open Quadratic Fermionic Systems
• Classifying transport behavior via current fluctuations in open quantum systems
• Response theory for nonequilibrium steady-states of open quantum systems
• Quantum response theory for nonequilibrium steady states
• Single-junction quantum-circuit refrigerator
• Dissipative Bose-Einstein condensation in contact with a thermal reservoir
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Linear response theory for quantum Gaussian processes
• Computational complexity of non-equilibrium steady states of quantum spin chains
• Symmetries and monotones in Markovian quantum dynamics
• Lindbladians with multiple steady states: theory and applications
• Linear response theory of Josephson junction arrays in a microwave cavity
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies