Energy spectra, density of energy levels, spin polarization, transport and optical properties of quantum dots and atomic traps

Abstract

A set of theoretical results [1-10] is reviewed, which concern calculations of energy spectra, density of energy levels, spin polarization, transport and optical properties (infrared absorption, luminescence) of semiconductor quantum dots and atomic traps. The studied systems contain a number of particles between 4 and 400, thus the calculation of their physical properties is a hard task. The analogy between these systems and the atomic nuclei is stressed and used throughout the paper. Common Nuclear Physics methods like Hartree-Fock and RPA schemes for finite systems, the BCS approach and the Lipkin-Nogami projection, and the Bethe-Goldstone equation were adapted to the present context. On the other hand, the Schrodinger equation was solved in basis with up to 40,000 functions by means of the Lanczos algorithm, and other methods like variational Monte Carlo estimations and two-point Pade approximants were also applied. Lastly, a stochastic projection of the BCS wave function was implemented.