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

## TL;DR

This paper develops a generalized master equation framework to analyze time-dependent transport in interacting mesoscopic systems, capturing Coulomb and electron-photon interactions, with applications to nanowires, quantum dots, and cavity-coupled systems.

## Contribution

It introduces a GME approach based on many-body states for realistic, interacting systems, including a Markovian version for cavity-coupled scenarios.

## Key findings

- Analyzed transient dynamics in a 2D nanowire.
- Observed Rabi oscillations in photocurrent.
- Explored thermoelectric properties in quantum dots.

## 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 get 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.