The TDA and RPA many-body methods are applied to a QCD motivated Hamiltonian in the Coulomb gauge. The gluon effects in the low energy domain are accounted for by the Instantaneous color-Coulomb Interaction between color-charge densities, approximated by the sum of a Coulomb (α/r) and a confining linear (βr) potentials. We use the eigenfunctions of the harmonic oscillator as a basis for the quantization of the quark fields, and discuss how suitable this basis is in various steps of the calculation. We show that the TDA results already reproduce the gross-structure of the light flavored meson states. The pion-like state in the RPA description, which is a highly collective state, is in a better agreement with the experimental value. The results are related to other nonperturbative treatments and compared to experimental data. We discuss the advantages of the present approach.

In this paper, we examine the effect of introducing a conical disclination on the thermal and optical properties of a two dimensional GaAs quantum dot in the presence of a uniform and constant magnetic field. In particular, our model consists of a single-electron subject to a confining Gaussian potential with a spin-orbit interaction in the Rashba approach. We compute the specific heat and the magnetic susceptibility from the exact solution of the Schrödinger equation via the canonical partition function, and it is shown that the peak structure of the Schottky anomaly is linearly displaced as a function of the topological defect. We found that such defect and the Rashba coupling modify the values of the temperature and magnetic field in which the system behaves as a paramagnetic material. Remarkably, the introduction of a conical disclination in the quantum dot relaxes the selection rules for the electronic transitions when an external electromagnetic field is applied. This creates a new set of allowed transitions causing the emergence of semi-suppressed resonances in the absorption coefficient as well as in the refractive index changes which are blue-shifted with respect to the regular transitions for a quantum dot without the defect.