Derivation of quantum master equation with counting fields by monitoring a probe

TL;DR

This paper derives a quantum master equation with counting fields using a microscopic model where a localized spin probe monitors electron current, enabling analysis of electron statistics and fluctuation theorems.

Contribution

It provides a novel microscopic derivation of a quantum master equation with counting fields incorporating a spin probe, linking current monitoring to quantum statistical analysis.

Findings

Derived a self-consistent quantum master equation with counting terms

Demonstrated the fluctuation theorem for electron current

Connected spin precession to electron counting statistics

Abstract

We show a microscopic derivation of a quantum master equation with counting terms which describes the electron statistics. A localized spin behaves as a probe whose precession angle monitors the net electron current by the magnetic-moment interaction. The probe Hamiltonian is proportional to the current, and is determined self-consistently for a model of a quantum dot. Then it turns out that the quantum master equation for the spin-precession contains the counting terms. As an application, we show the fluctuation theorem for the electron current.