We find it has the same behavior as that of the continuous phase transition in bcs super - conduction theory : the nonzero ground state energy gap decreases to zero at the finite critical temperature tsp , and the specific heat takes on divergence 我们发现该相变同bcs理论的连续相变极为相似：基态非零的能隙在有限的临界温度t _ ( sp )处降低为零，而比热呈现出趋于无穷的发散。
In the second part , the deduced self - energy in 63 theory is derived at hard thermal loop approximation . then we calculate the effective mass and damping rate , and also show that there is thermal instability above a critical temperature tc 在此基础上，出自能实部和虚部与一些介质效应的对应关系式，进而求得了粒子的有效质量和衰变率，并讨论了_ 6 ~ 3理论的热不稳定性。
For bose system , the critical temperature tc increase with atom number n . and we also found that the dimensionality had a great effect on such system . the condensate fraction is proportional to t3 in 3d , t2 in 2d , whereas t in 1d . this relation is hold for specific heat c 在谐振子势场的调制下，体系的基态粒子数所占的比重、比热均随温度t的d次幂变化，即n _ 0 n ， c t ~ d ，其中d为谐振子势场的维数。
Results show that the levitation force is generated between the high temperature superconductor and the magnetic field under the critical temperature . the value of the levitation force is determined by the temperature and the gradient of magnetic field . that is the smaller of the gap , the larger of the levitation force when the temperature is fixed , and the value of the levitation force is an exponential function of the gap 研究表明，当高温超导体的温度低于其临界温度时，在磁场中开始受到力的作用；受到的悬浮力大小由温度和磁场梯度共同决定；即温度一定时，悬浮间距越小，对应的磁场梯度越大，悬浮力就越大，力的大小与悬浮间距成指数关系；而当悬浮间距一定时，温度越低，对应的悬浮力也越大，且超导体刚进入超导态的一段温度区间悬浮力增大最快。
In this thesis , we use the random - matrix - theory to revise the following calculating methods : ( 1 ) the heat capacity and the spin susceptibility of the normal metallic small particles ; ( 2 ) the heat capacity of the conventional metallic small particles at the low temperature using the mean field approximation method ; ( 3 ) the heat capacity of the conventional metallic small particles at the vicinity of the critical temperature using the static path approximation method 本文采用随机矩阵理论，计算了： ( 1 )正常态金属小粒子的电子热容和顺磁磁化率。 ( 2 )在平均场近似下，计算了超导金属小粒子低温区的电子热容。 ( 3 )在静态路径近似下，计算了超导金属小粒子转变温区的电子热容。
