Out‐of‐Equilibrium Fluctuation‐Dissipation Relations Verified by the Electrical and Thermoelectrical AC‐Conductances in a Quantum Dot

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. 1600344 ( 1 of 9) www.advancedsciencenews.com www.ann-phys.org L R /[(ε − ε dc ) 2 + 2 ] is the transmission coefficient through the double barrier.

Getting information from the mixed electrical-heat noise

“…The out-of-equilibrium noise corresponds to the noise observed when there is no relation of order between the voltage, the frequency and the temperature. In that case, it has been shown [33] that we have for a quantum dot an equality between the total ac-conductance and the anti-symmetrized noise, summed over reservoirs, which is given by…”

“…(3). However, for frequency much higher than temperature, such a relation exists [33], and takes the form…”

“…It has been shown recently [33] that at temperature much higher than the voltage and frequency, k B T {eV, hω}, the mixed noise reads as…”

Axiomatic construction of quantum Langevin equations

“…For quantum examples, see [30]. [30,12,14]. Their discussion may require to trace precisely the several potential sources of noise present.…”

Electronic heat current fluctuations in a quantum dot

“…The issues raised by such studies are also of fundamental interest. The question of the generalization of the fluctuation-dissipation theorem to heat transport has been addressed [20][21][22] as well as the verification of the fluctuation theorem [11,[23][24][25][26][27] which is a microscopic extension of the second law of thermodynamics. The statistics of heat exchange in a driven open quantum system have been studied [28] as well as the statistics of work for a two-level system in the presence of dissipation [29].…”