Green-Kubo formulas with symmetrized correlation functions for quantum systems in steady states: the shear viscosity of a fluid in a steady shear flow

TL;DR

This paper extends the Green-Kubo formulas using symmetrized correlation functions to quantum systems in steady states, including those with work done on the system, exemplified by a fluid under steady shear flow.

Contribution

It generalizes the Green-Kubo formulas to quantum steady states with work input, linking fluctuation theorems to symmetrized correlation functions for induced quantities.

Findings

Derivation of Green-Kubo formulas for quantum systems with work input

Application to a fluid in steady shear flow

Validation of symmetrized correlation functions in quantum steady states

Abstract

For a quantum system in a steady state with a constant current of heat or particles driven by a temperature or chemical potential difference between two reservoirs attached to the system, the fluctuation theorem for the current was previously shown to lead to the Green-Kubo formula for the linear response coefficient for the current expressed in terms of the symmetrized correlation function of the current density operator. In this article, we show that for a quantum system in a steady state with a constant rate of work done on the system, the fluctuation theorem for a quantity induced in the system also leads to the Green-Kubo formula expressed in terms of the symmetrized correlation function of the induced quantity. As an example, we consider a fluid in a steady shear flow driven by a constant velocity of a solid plate moving above the fluid.