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

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.