Effective fluctuation theorems for electron transport in a double quantum dot coupled to a quantum point contact

TL;DR

This paper develops effective fluctuation theorems for electron transport in a double quantum dot system coupled to a quantum point contact, revealing how nonequilibrium conditions influence current statistics and thermodynamics.

Contribution

It introduces a non-perturbative theoretical framework for fluctuation theorems in a coupled quantum dot and point contact system, accounting for backaction and nonequilibrium effects.

Findings

Effective fluctuation theorems are established for DQD current.

The effective affinity can change sign due to QPC Coulomb drag.

Thermodynamic implications of the fluctuation theorems are discussed.

Abstract

A theoretical study is reported of electron transport at finite temperature in a double quantum dot (DQD) capacitively coupled to a quantum point contact (QPC). Starting from a Hamiltonian model, a master equation is obtained for the stochastic process taking place in the DQD while the QPC is at or away from equilibrium, allowing us to study the backaction of the QPC onto the DQD. The QPC is treated non-perturbatively in our analysis. Effective fluctuation theorems are established for the full counting statistics of the DQD current under different limiting conditions. These fluctuation theorems hold with respect to an effective affinity characterizing the nonequilibrium environment of the DQD and differing from the applied voltage if the QPC is out of equilibrium. The effective affinity may even change its sign if the Coulomb drag of the QPC reverses the DQD current. The thermodynamic implications of the effective fluctuation theorems are discussed.