A nonlinear Bloch model for Coulomb interaction in quantum dots

Brigitte Bidégaray-Fesquet (1) , Kole Keita (1)

1 EDP - Equations aux Dérivées Partielles

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.

Keywords: Maxwell-Bloch model; quantum dot; Coulomb interaction; Cauchy problem; Liouville model; positiveness properties

Domains: Mathematical Physics [math-ph]; Analysis of PDEs [math.AP]

Brigitte Bidégaray-Fesquet, Kole Keita. A nonlinear Bloch model for Coulomb interaction in quantum dots. 2012. ⟨hal-00738063v3⟩