Out-of-equilibrium fluctuation-dissipation relations verified by the electrical and thermoelectrical ac-conductances in a quantum dot

TL;DR

This paper verifies out-of-equilibrium fluctuation-dissipation relations in a quantum dot by analyzing electrical and thermoelectrical ac-conductances and their relation to noise, revealing conditions under which these relations hold.

Contribution

It demonstrates the generalized fluctuation-dissipation relations for a quantum dot out of equilibrium using ac-conductances and noise measurements, including numerical validation.

Findings

Electrical ac-conductance linked to electrical noise over reservoirs.

Thermoelectrical ac-conductance related to mixed noise with an energy step term.

Single reservoir fluctuation-dissipation relation applies at high frequencies.

Abstract

The electrical and heat currents flowing through a quantum dot are calculated in the presence of a time-modulated gate voltage with the help of the out-of-equilibrium Green function technique. From the first harmonics of the currents, we extract the electrical and thermoelectrical trans-admittances and ac-conductances. Next, by a careful comparison of the ac-conductances with the finite-frequency electrical and mixed electrical-heat noises, we establish the fluctuation-dissipation relations linking these quantities, which are thus generalized out-of-equilibrium for a quantum system. It is shown that the electrical ac-conductance associated to the displacement current is directly linked to the electrical noise summed over reservoirs, whereas the relation between the thermoelectrical ac-conductance and the mixed noise contains an additional term proportional to the energy step that the electrons must overcome when traveling through the junction. A numerical study reveals however that a fluctuation-dissipation relation involving a single reservoir applies for both electrical and thermoelectrical ac-conductances when the frequency dominates over the other characteristic energies.