Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes

TL;DR

This paper derives a raw Bloch model for light interaction with quantum boxes, ensuring positiveness and boundedness of solutions, which are crucial for future advanced mathematical analyses.

Contribution

It introduces a Liouville equation-based Bloch model that guarantees positiveness and boundedness, addressing limitations in previous models.

Findings

Ensures solutions are positive and bounded

Provides a rigorous derivation for quantum box interactions

Facilitates future mathematical studies of higher order effects

Abstract

The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena.