| Bose-Einstein condensation (BEC) has made great progress in the study of theory and experiment since it was observed in 1995. This thesis presents an introduction to the BEC and reviews the theoretical study on BEC of the Bose system in random box. The specific heat of the Bose gas in random box and the thermodynamic properties of the weakly interacting Bose gas in the gravitational field are investigated in detail.For the ideal Bose gas in random box, when the length of the box edge satisfies the bimodal and Gaussian distributions, respectively, the influence of the boundary conditions of the box on the specific heat is discussed. The results show that the specific heat is larger than that in a rigid box owing to the quenched fluctuation of the box edge, and increases with the increasing of the variation amplitude of the fluctuation. It means that the behavior of the system depends on the random boundary conditions. In addition, the specific heat is continuous at the critical temperature.For the weakly interacting Bose gas in the random box, the thermodynamic properties of the system are investigated using the mean field approximation. The results show that the critical temperature of the weakly interacting Bose gas in the random box is lower than that in a rigid box and the specific heat is larger than that in the rigid box. The gap of the specific heat at the critical temperature is found which is smaller than that of the rigid box, and decreases with the increasing of the variation amplitude of the fluctuation, and increases with the increasing of the interaction constant.For the ideal Bose gas in ultrarelativistic limit, the influence of the boundary conditions of the box on the specific heat is discussed. It indicates that the specific heat is larger than that in a rigid box, and increases with the increasing of the variation amplitude of the fluctuation. Meanwhile, the gap of the specific heat at the critical temperature is found under the ultrarelativistic limit, and it decreases with the increasing of the variation amplitude of the fluctuation.For the weakly interacting Bose gas in the gravitational field, the thermodynamic properties of the system are investigated with the mean field theory, including the density of states, the critical temperature and the ground-state population fraction. The results show that the critical temperature is lower than that of the ideal Bose gas in the gravitational field and the ground-state population fraction decreases when the scattering length is positive, and the situation is just opposite when the scattering length is negative. Meanwhile, the heat capacity is continuous at the transition temperature. |
