Fluctuation theorem for quantum electron transport in mesoscopic circuits

TL;DR

This paper investigates the fluctuation theorem in quantum electron transport within mesoscopic circuits, analyzing full counting statistics, effective affinities, and thermodynamic efficiencies in coupled quantum dot systems.

Contribution

It provides a microscopic derivation of fluctuation theorems for coupled quantum dot systems and explores conditions for single-current fluctuation theorems and thermodynamic efficiencies.

Findings

Joint probability distributions satisfy fluctuation theorems in the long-time limit.

Single-current fluctuation theorem holds for the slower channel at large current ratios.

Optimal efficiency at maximum power is achieved by tuning the quantum dot spectrum.

Abstract

We study the statistical properties of currents in two particular systems of capacitively coupled parallel transport channels. In the first system, each transport channel contains a single quantum dot in contact with two electron reservoirs. The second system we study is constituted of a double quantum dot coupled to two electrodes and probed by a quantum point contact detector. Thermodynamic forces are applied to each transport channel that generate fluctuating stationary currents. The full counting statistics of the currents is obtained starting from a microscopic Hamiltonian describing the electron dynamics. We verify that the joined probability distribution of the currents in each channel satisfies a fluctuation theorem in the long-time limit. The issue of single-current fluctuation theorems for the marginal distribution of the currents in one of the two channels is also investigated. We show that in the limit of large current ratio between both channels, a single-current fluctuation theorem is satisfied individually for the slower circuit in agreement with experimental observations. This theorem involves an effective affinity which depends on the thermodynamic forces applied to both channels and the specific features of the system considered. A detailed study of the effective affinity is made for the two aforementioned systems. Besides, we introduce a criteria on the initial condition of the transport channels for the observation of a fluctuation theorem at any time. This criteria is extended to the case of single-current fluctuation theorems. Finally, we perform the nonequilibrium thermodynamic analysis of a double quantum dot probed by a quantum point contact in the presence of temperature and chemical potential differences between the electrodes. A thermal machine is studied and shown to reach highest efficiencies at maximum power by fine tuning the double quantum dot spectrum.