The Study Of Bose-Einstein Condensation In The Relativistic Gas

Recently, Bose-Einstein condensation (BEC) is extensively studied in theory and experiment. In this thesis, Using semi-classical approximation method, the properties of a relativistic Bose gas is investigated.The BEC and thermodynamic properties of the relativistic ideal Bose gas (RIBG) in random box are studied. When the length of the box edge satisfies the bimodal and Gaussian distributions, respectively, the transition temperature T_c and the Helmholtz free energy of the system at T_c are studied. The results indicate that T_c of the system is lowered by the presence of quenched disorder. In addition, the phase diagram of the system is obtained. We find that for the temperature close to the rigid box transition, a small disorder can result in the destruction of the condensation.The behavior of the RIBG with antibosons in random box is investigated. The results show that T_c of the system with antibosons is lowered by the disorder as well. However, comparing to the case of the system without antibosons, T_c of the system with antibosons is higher than that of the system without antibosons. It implies that the system with antibosons is more stable. In addition, the behavior of the fluctuation of the box edge is similar to that of the system without antibosons.The BEC and thermodynamic properties of the relativistic harmonic oscillator are studied. T_c and the Helmholtz free energy of the system at T_c are calculated. The effect of the rest mass of boson on the properties of the system is discussed. The results show that the larger the number of bosons is, the higher the transition temperature is, and the lower the Helmholtz free energy at T_c is. While for a given value of the number of bosons, the smaller the rest mass of boson is, the higher the transition temperature is, and the lower the Helmholtz free energy at T_c is.The effect of antibosons on the behavior of a relativistic Bose gas in harmonic traps is investigated. The results show that the behaviors of T_c and the Helmholtz free energy at T_c are similar to that of the system without antibosons. However, for a given value of the number of the bosons, T_c of the system with antibosons is higher than that of the system without antibosons, and the Helmholtz free energy at T_c of the system with antibosons is lower than that of the system without antibosons. This means that the system with antibosons is more stable.