Effects of finite temperature in ballistic quantum dots

We studied the effects of finite temperature in the magnetic susceptibility of a system of non-interacting electrons in a homogeneous magnetic field and in a smooth confinement potential: the two-dimensional harmonic oscillator. Different exact ensemble calculations are considered and discussed: canonical ( fixed), canonical via grand-canonical ( average fixed) and partial canonical ensembles. We compute a Gaussian average of the susceptibility over the number of particles and another one over the size of system in order to compare our results with data of mesoscopic systems experiments. We conclude that it is fundamental to consider interactions between the particles in the theoretical analysis to obtain the temperature dependence of the experimental results.