This is the repository for the QMC Project @ UiO, Autumn 2014. The current branch is an extension of the original project, meant to be presented as a BSc Thesis at the University of Trento
The aim of this project is to use the variational Monte Carlo (VMC) method to evaluate the ground state energy, one-body densities, expectation values of the kinetic and potential energies and single-particle energies of quantum dots with $N = 2$ and $N = 6$ electrons, so-called closed shell systems.
We will begin with two electrons confined in a pure two-dimensional isotropic harmonic oscillator potential, with and without the repulsive interaction, developing a simple trial wave-function and a basic program that runs our calculations. Then we are going to improve the trial wave-function adding the so-called Jastrow factor, and finally we are going to extend the entire class of wave-functions and the program itself to a given number of electrons (obviously, for a closed-shell system). After that we are going to improve our sampling, switching from a brute-force approach to the clever importance sampling.
In addition, we will present a method that implements analytical derivatives for calculating both the energy and the diffusive force of the importance sampling.
Matteo Seclì ([email protected])
