Confined quantum systems in one dimension and conductance oscillations in narrow channels

An exactly solvable electron model of a confined system with inverse-square interaction is presented. The ground state is given by the Jastrow-product wavefunction of power-law form. We discuss the results in connection with conductance oscillations observed in semiconductor nanostructures, for which single-electron charging effects play a crucial role. Due to the internal spin degrees of freedom, there appear two independent periods of the conductance oscillations in very narrow channels even at zero temperature.