A semiclassical approach to the ground state and density oscillations of quantum dots

TL;DR

This paper develops a semiclassical Thomas-Fermi approach with gradient corrections to model ground states and density oscillations in 2D quantum dots, validated against microscopic solutions.

Contribution

It introduces a semiclassical method incorporating gradient terms for analyzing quantum dots, bridging classical and quantum descriptions.

Findings

Accurate ground state descriptions for 2D nanostructures.

Effective modeling of density oscillations.

Good agreement with microscopic Kohn-Sham solutions.

Abstract

A semiclassical Thomas-Fermi method, including a Weizs\"acker gradient term, is implemented to describe ground states of two dimensional nanostructures of arbitrary shape. Time dependent density oscillations are addressed in the same spirit using the corresponding semiclassical time-dependent equations. The validity of the approximations is tested, both for ground state and density oscillations, comparing with the available microscopic Kohn-Sham solutions.