Defining the effective temperature of a quantum driven system from current-current correlation functions

TL;DR

This paper derives a method to define an effective temperature in quantum driven systems using current-current correlation functions and compares it with other temperature definitions, revealing their equivalence at low frequencies.

Contribution

It introduces a fluctuation-dissipation relation for current correlations to define an effective temperature in quantum systems driven by time-dependent voltages.

Findings

Effective temperature coincides with local and single-particle temperatures at low frequencies.

Derived an expression for zero-frequency noise in multiterminal quantum systems.

Proposed a fluctuation-dissipation relation applicable to driven quantum systems.

Abstract

We calculate current-current correlation functions and find an expression for the zero-frequency noise of multiterminal systems driven by harmonically time-dependent voltages within the Keldysh non-equilibrium Green's functions formalism. We also propose a fluctuation-dissipation relation for current-current correlation functions to define an effective temperature. We discuss the behavior of this temperature and compare it with the local temperature determined by a thermometer and with the effective temperature defined from a single-particle fluctuation-dissipation relation. We show that for low frequencies all the definitions of the temperature coincide.