Shell structures and level statistics of a quantum dot

We have investigated the level fluctuations of a two-dimensional quantum dot reflected in the addition energy spectrum. The level degeneracy consistent with the rotational symmetry of the confining potential determines the structure of the energy shells. In the limit that the energy level spacings are significant compared to the electron-electron interaction energy, we find that the addition energy spectrum clearly displays the atomic magic numbers. Even in the opposite limit a closed shell state of a dot can give rise to large level fluctuations. When a strong magnetic field is present these fluctuations are significantly reduced.