Interacting electrons in a one-dimensional quantum dot

The spectral properties of up to four interacting electrons confined within a quasi-one-dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground-state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest-lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.