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 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.

39 pages, 13 figures

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Cited by in corpus (4)

• The effects of a far-infrared photon cavity field on the magnetization of a square quantum dot array
• Self-induction and magnetic effects in electron transport through a photon cavity
• Quantum turnstile regime of nanoelectromechanical systems
• Controlling thermoelectric, heat, and energy currents through a quantum dot in sequential and cotunneling Coulomb-blockade regimes