Shell structures and level statistics of a quantum dot

We have investigated the level fluctuations of a two-dimensional quantum do t reflected in the addition energy spectrum. The level degeneracy consisten t with the rotational symmetry of the confining potential determines the st ructure of the energy shells. In the limit that the energy level spacings a re significant compared to the electron-electron interaction energy, we fin d that the addition energy spectrum clearly displays the atomic magic numbe rs. 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.