Properties Of The Heat Capacity Of Small Metallic Grains

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.Drawing the following concludes:(1) For the different metallic small particles with even number or odd number, the heat capacity is varied. The result is different from the bulk metal in essence. At the low temperature, the distribution of the discrete energy levels has important effects on the heat capacity; at the high temperature, the distribution of the discrete energy levels has little effects because of the involving of mass electrons into the energy distribution. As to the spin susceptibility, it has the same tendency as the heat capacity.(2) For small size particles, the heat capacity within the BCSexhibits a jump at T =TC as the bulk particles (d =0),butwith the various spin, the amplitude of the jump is varied. At the low temperature, the heat capacity is related to the particles with even number or odd number, after the critical temperature, the heat capacity conforms with the normal particles' values.(3) For decreasing sizes, the fluctuation becomes more and more significant at the vicinity of the critical temperature; the even-odd effect is important at the low temperature and the vicinity of the critical temperature as well.