nicolossus / fys4411-project1

FYS4411 - Computational Physics II: Quantum Mechanical Systems

Project 1:

This repository contains programs, material and report for project 1 in FYS4411 made in collaboration between Jørn Eirik, Nicolai and Aleksandar.

In this project, we build a variational Monte Carlo method to estimate the ground state energy of an ultracold, dilute Bose gas in harmonic traps. We use a trial wave function composed of a single particle Gaussian with a single variational parameter and a hard sphere Jastrow factor for pair correlations. We consider two Markov chain Monte Carlo sampling algorithms; a random walk Metropolis with Gaussian proposals and a Langevin Metropolis-Hastings with proposals driven according to the gradient flow of the probability density of the trial wave function. The methods are implemented in a Python framework with automatic differentiation, procedures for tuning scale parameters and gradient descent optimizations of the variational parameter. The blocking method, which accounts for the autocorrelation of a Markov chain, is used to calculate the statistical error of the variational energy. Our vmc package can be found in the src directory.

Contents

The data directory contains raw data from simulations.

The latex directory contains the LaTeX source for building the report, as well as figures and tables generated in the analyses.

The notebooks directory contains Jupyter Notebooks used in the analyses.

The report directory contains the report rendered to PDF from the LaTeX source.

The resources directory contains project resources such as literature.

The simulation_scripts directory contains programs that run particular simulations and store the results for further analyses.

The src directory contains the source code of the vmc package.

The tests folder contains unit tests. Run tests locally with pytest:

$ pytest tests -v -W ignore

Virtual environment

environment.yml contains the dependencies of the vmc package, including JAX used for automatic differentiation. Install the conda environment:

$ conda env create --file environment.yml

To activate the environment:

$ conda activate bios1100

To deactivate the environment:

$ conda deactivate