Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems - Abstract

Wilhelm, Lukas

An abstract approach to the Landauer-Büttiker formula with application to an LED toy model

We give a new derivation of the Landauer-Büttiker formula that is inspired by the work of Nenciu, but that does not make use of generalized eigenfunctions or the Lippmann-Schwinger equation. We stay in a purely operator theoretical framework, and our results are even valid for perturbations that are only locally trace class. We then present a toy model for a quantum dot LED to which this derivation can be applied to obtain a Landauer-Büttiker type formula for the electron current in the presence of electron-photon interaction.