Finite size effects on the bose-einstein condensation

In this thesis, the finite size effects for the Bose-Einstein condensation are investigated. The application of the Poisson summation method on the ideal Bose gas (both for relativistic and non-relativistic cases) is studied. The Bose gas is assumed to be enclosed in a cubical finite enclosure with periodic boundary conditions. The Bogoliubov theory for the weakly interacting Bose gas is reviewed and an expression for the ground state energy in terms of the heat kernel is obtained. We observed that a well known result of the ground state energy is obtainable via an alternative method. Then for the zero temperature case, the depletion of the condensate is treated with the heat kernel analysis combined with the Poisson summation method. The results show that for such conguration, finite size corrections turn out to be of order 1=L^2. Finally, for the zero temperature case, the ground state energy is analysed by scaling the heat kernel. This yields finite size corrections of order 1/L, a result which shows the necessity of a more elaborate treatment for more accurate results.