Effective Equilibrium in Out-of-Equilibrium Interacting Coupled Nanoconductors.

Lucas Maisel,Rosa López

doi:10.3390/e22010008

Abstract

In the present work, we study a mesoscopic system consisting of a double quantum dot in which both quantum dots or artificial atoms are electrostatically coupled. Each dot is additionally tunnel coupled to two electronic reservoirs and driven far from equilibrium by external voltage differences. Our objective is to find configurations of these biases such that the current through one of the dots vanishes. In this situation, the validity of the fluctuation–dissipation theorem and Onsager’s reciprocity relations has been established. In our analysis, we employ a master equation formalism for a minimum model of four charge states, and limit ourselves to the sequential tunneling regime. We numerically study those configurations far from equilibrium for which we obtain a stalling current. In this scenario, we explicitly verify the fluctuation–dissipation theorem, as well as Onsager’s reciprocity relations, which are originally formulated for systems in which quantum transport takes place in the linear regime.

Highlights

The two paradigms of statistical mechanics for systems that are close to equilibrium are: (i) the Onsager–Casimir reciprocity relations [1]; and (ii) the fluctuation–dissipation theorem (FDT) [2,3,4]
Returning to our purpose, which is to find a route to an effective equilibrium state, we address the issue of whether the opposite phenomenon to the drag is possible, i.e., if we can achieve a non-equilibrium configuration with V1 6= V2 for which the drag effect causes the stalling of the upper currents
We explored the fulfilment of Equation (29) when stalling currents are present in the system, with Gαβγ again computed with help of Full Counting Statistics (FCS)

Summary

Introduction

The two paradigms of statistical mechanics for systems that are close to equilibrium are: (i) the Onsager–Casimir reciprocity relations [1]; and (ii) the fluctuation–dissipation theorem (FDT) [2,3,4].Both relations are inherent to classical systems but are applicable to the quantum regime.The Onsager–Casimir reciprocity relations state that the Onsager matrix that relates physical fluxes and their conjugate forces is symmetric. The two paradigms of statistical mechanics for systems that are close to equilibrium are: (i) the Onsager–Casimir reciprocity relations [1]; and (ii) the fluctuation–dissipation theorem (FDT) [2,3,4] Both relations are inherent to classical systems but are applicable to the quantum regime. In the context of quantum transport through electronic nanodevices, the FDT allows us to relate the dissipative response of one current with respect to a variation of its affinity or conjugate force with its spontaneous fluctuations. This property of equilibrium systems is a very important topic when we are interested in controlling dissipation due to currents induced through quantum conductors by external forces

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Conclusion