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. Introduction Interaction effects play a crucial role in the understanding of the electrical transport properties of very small condensed matter systems at low temperatures [1]. Examples are • the Coulomb Blockade [2, 3], where charging energies of single electrons suppress the current through a dissipatively shunted tunnel junction • Single Electron Tunneling oscillations [4] of the voltage across such a junction at constant current