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

TL;DR

This paper reviews theoretical calculations of energy spectra, spin polarization, and optical properties of quantum dots and atomic traps, highlighting methods adapted from nuclear physics and advanced computational techniques for systems with up to 400 particles.

Contribution

It introduces novel adaptations of nuclear physics methods and computational algorithms to analyze complex quantum dot and atomic trap systems with many particles.

Findings

Energy spectra and optical properties are successfully calculated for systems with 4-400 particles.

Advanced computational methods like Lanczos algorithm and Monte Carlo are effectively applied.

Analogies with nuclear physics provide new insights into quantum dot properties.

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.