Properties Of The Electronic Heat Capacity Of Small Metallic Grains In The Magnetic Field

The heat capacity of small metallic grains at some typical temperature in the magnetic field by considering the effects of energy level distribution and parity were caculated by Random Matrix Theory.ln the paper we treat the energy level distribution with 3 different statistical ensambles(GOE,GSE,GUE).Then we make some simple analysis to the changing of the heat capacity with the magnetic field. Some theorical results are caculated as follows:(1) For the different normal metallic small particles with even or odd number of electrons, the heat capacity is different from 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 level distribution has little effects because of the involving of mass electrons into the distribution.(2) Magnetic field can inaease the heat capacity of small metallic grains.yet it displays on the feature of quasi periodicity.Under the 3 different statistical ensambles(GOE,GSE,GUE),the heat capacity of small metallic grains changes almost as the same.Under the same temperature and magnetic field, the heat capacity will increase with the sequence of GOE→ GUE→ GSE.(3) In magnetic field, to different metallic small particles with even number or odd number the heat capacity is varied. And the magnetic field affects the heat capacity of metallic small particles with odd number more than that with even number. This is also different from the bulk metal in essence.(4) The heat capacity increases with the increasing diamerer of small metallic grains.The quanta size offect will disappear and when the diameter of the small metallic grains reaches a certain degree (i.e.δ >k_BT) then properties of the electronic heat capacity ofsmall metallic grains in the magnetic field will be the same as that in bulk metal.