The effect of level statistics and fluctuations on the specific heat of small metallic superconducting grains

The thermodynamic properties of small metallic superconducting grains are affected by fluctuations in the order parameter and the level statistics, especially in the critical region. Here, the static path approximation was applied to deal with the fluctuations and the thermodynamic contribution of quasiparticles, and random matrix theory was applied to deal with level statistics. The specific heats were calculated numerically in the cases of even and odd number of electrons and different spins.