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

### **Valeriu Moldoveanu 1,\*, Andrei Manolescu 2 and Vidar Gudmundsson 3**


Received: 17 June 2019; Accepted: 23 July 2019; Published: 25 July 2019

**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 states provides the suitable formal framework to capture both the effects of the Coulomb interaction and electron–photon coupling due to a surrounding single-mode cavity. We outline the derivation of this equation within the Nakajima–Zwanzig formalism and point out technical problems related to its numerical implementation for more realistic systems which can neither be described by non-interacting two-level models nor by a steady-state Markov–Lindblad equation. We first solve the GME for a lattice model and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamical onset of the current-current correlations in electrostatically coupled parallel quantum dots and transient thermoelectric properties. Secondly, we rely on a continuous model to ge<sup>t</sup> the Rabi oscillations of the photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity. A many-body Markovian version of the GME for cavity-coupled systems is also presented.

**Keywords:** time-dependent transport; electron–photon coupling; open quantum systems
