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

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