The Theoretical Study Of The Bose Gas In The Gravitational Field

The external potential plays an important role in the behavior of the Bose gas. Recently, Bose-Einstein condensation (BEC) is extensively studied in theory and experiment. In this thesis, we investigate the condensation of the Bose gas and its thermodynamic properties in the gravitational field.For the ideal Bose gas in the gravitational field, the BEC and the thermodynamic properties of the systems are studied. Using the semi-classical approximation, the thermodynamic quantities, such as, the transition temperature, the density of the states, the heat capacity and the entropy of the system are all calculated. It is showed that for one- , two- and three-dimensional systems in the gravitational field, there is BEC. Meanwhile, the continuity of the heat capacity at the critical temperature is studied. We found that for the one- and two-dimensional systems, the heat capacity is continuous at the critical temperature, but for the three-dimensional case, there is a gap at the critical temperature. What is more, we discussed the entropy of the system. It is found that the entropy increases with the increasing of the temperature.For the relativistic ideal Bose gas (RIBG) in the gravitational field, the BEC is discussed by means of the semi-classical approximation. For the non-relativistic (NR) and ultra-relativistic (UR) extremes, the transition temperature, the fraction of the ground state and the heat capacity of the system are calculated. The behavior of the continuity of the heat capacity at the critical temperature is investigated. The result showed that for the one-dimensional system, the heat capacity is continuous at the critical temperature in both non-relativistic (NR) and ultra-relativistic (UR) extremes, for the two-dimensional system, it is continuous in non-relativistic extreme, but for the ultra-relativistic (NR) case, there is a gap of the heat capacity. While for the three-dimensional case, there is a gap of the heat capacity at the critical temperature in both non-relativistic (NR) and ultra-relativistic (UR) extremes. We also found that the gap of the ultra-relativistic (UR) extreme is larger than that of the non-relativistic extreme.For the weakly interacting relativistic Bose gas in the gravitational field, the thermodynamic properties of the systems are investigated using the local density approximation. The thermodynamic quantities, such as the transition temperature, heat capacity and so on, are calculated. The results showed that for the weakly interacting Bose gas, the transition temperature is lower than that of the ideal Bose gas in the both non-relativistic (NR) and ultra-relativistic (UR) extremes. It means that the repulsive interaction hinders the condensation. We also found that the heat capacity of the weakly interacting system is lower than that of the ideal boson gas.