Properties of a Bose Gas in the Presence of Disorder (Laurea thesis)

TL;DR

This thesis investigates how disorder affects Bose-Einstein condensation and superfluidity in a Bose gas, using computational and analytical methods to explore ground state properties and phase behavior at zero temperature.

Contribution

It develops a detailed Diffusion Monte Carlo approach and compares it with Bogoliubov theory to analyze disorder effects on superfluid and condensate fractions in Bose gases.

Findings

Superfluid fraction can be smaller than condensate fraction in disordered Bose gases.

DMC results agree with Bogoliubov theory at low disorder strength.

Ground state energy predictions match DMC calculations in the weak disorder regime.

Abstract

The phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas with disorder is investigated. Diffusion Monte Carlo (DMC) method is used to calculate superfluid and condensate fraction of the system as a function of density and strength of disorder at zero temperature. The algorithm and implementation of the Diffusion Monte Carlo method is explained in details. Bogoliubov theory is developed for the analytical description of the problem. Ground state energy, superfluid fraction and condensate fraction are calculated. It is shown that same results for the superfluid fraction can be obtained in a perturbative manner from Gross-Pitaevskii equation. Ground state energy, obtained from DMC calculations, is compared to predictions of Bogoliubov theory, which are found to be valid in the regime, when the strength of disorder is small. It is shown that "unusual" situation, when the superfluid fraction is smaller than the condensate fraction, can be realized in this system.