Generalized Master Equation Approach to Time-Dependent Many-Body Transport

Abstract

We recall theoretical studies on transient transport through interacting mesoscopic systems.It is shown that a generalized master equation (GME) written and solved in terms of many-body statesprovides the suitable formal framework to capture both the effects of the Coulomb interaction andelectron–photon coupling due to a surrounding single-mode cavity. We outline the derivation of thisequation within the Nakajima–Zwanzig formalism and point out technical problems related to itsnumerical implementation for more realistic systems which can neither be described by non-interactingtwo-level models nor by a steady-stateMarkov–Lindblad equation. We first solve the GME for a latticemodel and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamicalonset of the current-current correlations in electrostatically coupled parallel quantum dots and transientthermoelectric properties. Secondly, we rely on a continuous model to get the Rabi oscillations ofthe photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity.A many-bodyMarkovian version of the GME for cavity-coupled systems is also presented.