Applications of nonequilibrium Kubo formula to the detection of quantum noise

TL;DR

This paper extends the Kubo fluctuation-dissipation theorem to nonequilibrium stationary states, demonstrating its application in quantum noise detection and deriving generalized current commutation relations for fermionic and bosonic systems.

Contribution

It provides a simple proof of the nonequilibrium Kubo relation and applies it to quantum noise measurement and current commutation relations in stationary states.

Findings

Nonsymmetrized noise power spectrum is measured in excess noise experiments.

Derived a generalized commutation relation for fermionic and bosonic currents.

Extended the fluctuation-dissipation theorem to nonequilibrium stationary states.

Abstract

The Kubo fluctuation-dissipation theorem relates the current fluctuations of a system in an equilibrium state with the linear AC-conductance. This theorem holds also out of equilibrium provided that the system is in a stationary state and that the linear conductance is replaced by the (dynamic) conductance with respect to the non equilibrium state. We provide a simple proof for that statement and then apply it in two cases. We first show that in an excess noise measurement at zero temperature, in which the impedance matching is maintained while driving a mesoscopic sample out of equilibrium, it is the nonsymmetrized noise power spectrum which is measured, even if the bare measurement, i.e. without extracting the excess part of the noise, obtains the symmetrized noise. As a second application we derive a commutation relation for the two components of fermionic or bosonic currents which holds in every stationary state and which is a generalization of the one valid only for bosonic currents. As is usually the case, such a commutation relation can be used e.g. to derive Heisenberg uncertainty relationships among these current components.