Strongly correlated confined electrons

A few-electron system, as realized in semiconducting quantum dots, is investigated. Numerical results for the charge density distribution in quasi one-dimensional (1D) systems reveal three characteristic regimes of electron densities. At low carrier densities the ground state and the collective excitations correspond to those of a finite Wigner crystal. At intermediate densities low energy excitations involving the spin occur in 1D and 2D. They are investigated using correlated ''pocket state'' basis functions. For non-isotropic confining potentials and sufficiently large mean electron distances r(s) this method becomes exact. The ratios between the lowest energy excitation energies are determined quantitatively using group theoretical methods. They are independent of the detailed form of the electron-electron repulsion potential and of r(s). The results of the pocket state apprach are compared with available numerical data. Transport through a quantum dot is investigated under Coulomb blockade conditions for weak coupling to perfect leads. A master equation approach allows to incorporate nonequilibrium properties at finite applied voltages as well as spin selection rules for the transitions between the correlated many electron states. A model for the recently discovered negative differential conductances is proposed. Asymmetries in the transport is predicted for asymmetric dot-lead coupling. Recent experimental results for in-plane magnetic fields can be described by the Zeeman-splitting of the many electron states.