Optical absorption and addition spectra of an N-electron quantum dot: An algebraic Hamiltonian approach

We calculate analytically the energies of a class of N-electron quantum dots employing a recently introduced symplectic-group chain. The corresponding algebraic Hamiltonians lie beyond the N-electron Fock-Darwin Hamiltonian which only describes noninteracting particles in a perfect parabolic confining potential. Nonparabolicity and particle-particle interactions are simulated using quadratic Casimir operators within the symplectic-group chain. We calculate infrared optical absorption energies as a function of magnetic field, and analyze the breakdown of the generalized Kohn theorem. We also calculate the addition spectra associated with transport through the N-electron quantum dot.