Generalized Master Equation Approach toTime-Dependent Many-Body Transport

• Published in: Entropy
• Main Authors: Moldoveanu, Valeriu, Manolescu, Andrei, Gudmundsson, Vidar
• Other Authors: Tækni- og verkfræðideild (HR), School of Science and Engineering (RU), Háskólinn í Reykjavík, Reykjavik University
• Format: Article in Journal/Newspaper
• Language: English
• Published: MDPI AG 2019
• Subjects: General physics and astronomy; Time-dependent transport; Electron-photon coupling; Open quantum systems; Electron transport; Photons; Electrons; Mathematical models; Markov processes; Electromagnetic coupling; Eðlisfræði; Skammtafræði; Rafeindir; Ljóseindir; Reiknilíkön; Markovferli; Rafsegulfræði; Iceland; Reykjavik University
• Online Access: https://hdl.handle.net/20.500.11815/1900; https://doi.org/10.3390/e21080731

Publisher's version (útgefin grein). 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. The Research Fund of the University of Iceland, the Icelandic Research Fund, grant no. 163082-051, the Icelandic Instruments Fund, and Reykjavik University, grant no. 815051. Some of the computations were performed on resources provided by the Icelandic High Performance Computing Centre at the University of Iceland. V. M. also acknowledge financial support from CNCS-UEFISCDI grant PN-III-P4-ID-PCE-2016-0084 and from the Romanian Core Program PN19-03 (contract no. 21 N/08.02.2019) "Peer Reviewed"