From non-equilibrium Green's functions to quantum master equations for the density matrix and out-of-time-order correlators: steady state and adiabatic dynamics

TL;DR

This paper derives quantum master equations for the density matrix and out-of-time-order correlators in a driven, open quantum system using non-equilibrium Green's functions, focusing on steady state and adiabatic dynamics.

Contribution

It provides a systematic derivation of these equations from microscopic Hamiltonians, incorporating adiabatic response and coherent effects, for the first time in this context.

Findings

Derived master equations for density matrix and correlators.

Calculated particle and energy fluxes in specific models.

Highlighted the role of coherence in open quantum systems.

Abstract

We consider a finite quantum system under slow driving and weakly coupled to thermal reservoirs at different temperatures. We present a systematic derivation of the quantum master equation for the density matrix and the out-of-time-order correlators. We start from the microscopic Hamiltonian and we formulate the equations ruling the dynamics of these quantities by recourse to the Schwinger-Keldysh non-equilibrium Green's function formalism, performing a perturbative expansion in the coupling between the system and the reservoirs. We focus on the adiabatic dynamics, which corresponds to considering the linear response in the ratio between the relaxation time due to the system-reservoir coupling and the time scale associated to the driving. We calculate the particle and energy fluxes. We illustrate the formalism in the case of a qutrit coupled to bosonic reservoirs and of a pair of interacting quantum dots attached to fermionic reservoirs, also discussing the relevance of coherent effects.