A nonlinear Bloch model for Coulomb interaction in quantum dots

TL;DR

This paper develops a nonlinear Bloch model incorporating Coulomb interactions in quantum dots, coupling it with Maxwell equations, and discusses the implications of neglecting intra-band coherences through numerical analysis.

Contribution

It introduces a nonlinear Bloch model for Coulomb interactions in quantum dots and couples it with Maxwell equations, providing new insights into intra-band coherence effects.

Findings

Numerical results demonstrate the impact of Coulomb interactions.

Discussion on the validity of neglecting intra-band coherences.

Enhanced understanding of electron-electron interactions in quantum dots.

Abstract

In this paper we first derive a Coulomb Hamiltonian for electron--electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix. The coupling with Maxwell equations when interaction with an electromagnetic field is also considered from the Cauchy problem point of view. The study is completed by numerical results and a discussion about the advisability of neglecting intra-band coherences, as is done in part of the literature.