Level Fluctuations and Many-Body Effects in Disorder-Free Quantum Dots

We have investigated whether many-body effects can induce significant level fluctuations in a disorder-free quantum dot. The closed energy shell structures and relaxation of the Hartree-Fock potentials are found to play a significant role. The level degeneracy consistent with the rotational symmetry of the confining potential determines the structure of the energy shells. A closed shell state of a dot can give rise to large fluctuations. When a strong magnetic field is present the shell structure is absent and fluctuations are significantly reduced.