Optical properties of charged quantum dots doped with a single magnetic impurity

We present a microscopic theory of the optical properties of self-assembled quantum dots doped with a single magnetic manganese (Mn) impurity and containing a controlled number of electrons. The single-particle electron and heavy-hole electronic shells are described by two-dimensional harmonic oscillators. The electron-electron, electron-hole Coulomb as well as the short-range electron spin-Mn spin and hole spin-Mn spin contact exchange interactions are included. The electronic states of the photo-excited electron-hole-Mn complex and of the final electron-Mn complex are expanded in a finite number of configurations and the full interacting Hamiltonian is diagonalized numerically. The emission spectrum is predicted as a function of photon energy for a given number of electrons and different number of confined electronic quantum dot shells. We show how emission spectra allow to identify the number of electronic shells, the number of electrons populating these shells and, most importantly, their spin. We show that electrons not interacting directly with the spin of Mn ion do so via electron-electron interactions. This indirect interaction is a strong effect even when Mn impurity is away from the quantum dot center.Comment: 12 pages, 10 figure

Linear Form of 3-scale Relativity Algebra and the Relevance of Stability

We show that the algebra of the recently proposed Triply Special Relativity can be brought to a linear (ie, Lie) form by a correct identification of its generators. The resulting Lie algebra is the stable form proposed by Vilela Mendes a decade ago, itself a reapparition of Yang's algebra, dating from 1947. As a corollary we assure that, within the Lie algebra framework, there is no Quadruply Special Relativity.Comment: 5 page

Dirac quantization of a nonminimal gauged O(3) sigma model

The (2+1) dimensional gauged O(3) nonlinear sigma model with Chern-Simons term is canonically quantized. Furthermore, we study a nonminimal coupling in this model implemented by means of a Pauli-type term. It is shown that the set of constraints of the model is modified by the introduction of the Pauli coupling. Moreover, we found that the quantum commutator relations in the nominimal case is independent of the Chern-Simons coefficient, in contrast to the minimal one.Comment: 7 pages, to appear in Modern Physics Letters

Supersymmetrization of the Radiation Damping

We construct a supersymmetrized version of the model to the radiation damping \cite{03} introduced by the present authors \cite{ACWF}. We dicuss its symmetries and the corresponding conserved Noether charges. It is shown this supersymmetric version provides a supersymmetric generalization of the Galilei algebra obtained in \cite{ACWF}. We have shown that the supersymmetric action can be splited into dynamically independent external and internal sectors.Comment: 9 page