Determination of ground state energy and effective mass of bose systems in random potentials by path integration method

Abstract

We apply Feynman's path integral theory to study Bose-Einstein condensates in a double well potential and in a random potential. The main idea of this thesis is to perform the mean field approximation in two body interaction by the path integral approach. Bose particles are confined in the double well which is taken as a harmonic potential with Gaussian or cosine barrier. Performing the variational calculations we obtain analytical results of the ground state energy, wave functions, and overlap integrals. The overlap integrals enable us to calculate the tunneling rates which are in good agreement with numerical values for the two-mode model of Gross-Pitaevskii's equation. We also consider the model of a Bose system consisting of N particles with finite interacting pair potentials under the influence of random potentials. The porosity or nonhomogeneity of the system can be represented by the density of porosity with amplitude of the fluctuation, and a correlation length. We obtain analytical results of the effective mass and the ground state energy which are in good agreement with that of Bugoliubov approach. The propagator of the system is used to calculate the partition function, specific heat, the critical temperature, condensate density, and the superfluid density of the system.