# Universality in the Energy Spectrum of Medium-Sized Quantum Dots - Condensed Matter > Mesoscale and Nanoscale Physics

Universality in the Energy Spectrum of Medium-Sized Quantum Dots - Condensed Matter > Mesoscale and Nanoscale Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: In a two-dimensional parabolic quantum dot charged with $N$ electrons,Thomas-Fermi theory states that the ground-state energy satisfies the followingnon-trivial relation: $E {gs}-\hbar\omega\approx N^{3-2}f {gs}N^{1-4}\beta$, where the coupling constant, $\beta$, is the ratiobetween Coulomb and oscillator $\hbar\omega$ characteristic energies, and$f {gs}$ is a universal function. We perform extensive ConfigurationInteraction calculations in order to verify that the exact energies ofrelatively large quantum dots approximately satisfy the above relation. Inaddition, we show that the number of energy levels for intraband and interbandexcitonic and biexcitonic excitations of the dot follows a simple exponentialdependence on the excitation energy, whose exponent, $1-\Theta$, satisfies alsoan approximate scaling relation {\it a la} Thomas-Fermi,$\Theta-\hbar\omega\approx N^{-\gamma} gN^{1-4}\beta$. We provide ananalytic expression for $f {gs}$, based on two-point Pad\-e approximants, andtwo-parameter fits for the $g$ functions.

Author: ** Alexander Odriazola 1, Alain Delgado 2, Augusto González 1 1 Instituto de Cibernética, Matemática y Física, Habana, 2 Centro **

Source: https://arxiv.org/