  Recently, the electron transport through a quasi-one dimensional (quasi-1D)
electron gas was investigated experimentally as a function of the confining
potential. We present a physical model for quantum ballistic transport of
electrons through a short conduction channel, and investigate the role played
by the Coulomb interaction in modifying the energy levels of two-electron
states at low temperatures as the width of the channel is increased. In this
regime, the effect of the Coulomb interaction on the two-electron states has
been shown to lead to four split energy levels, including two anti-crossings
and two crossing-level states. Due to the interplay between the anti-crossing
and crossing of the energy levels, the ground state for the two-electron model
switches from one anti-crossing state for strong confinement to a crossing
state for intermediate confinement as the channel width is first increased, and
then returned to its original anti-crossing state. This switching behavior is
related to the triplet spin degeneracy as well as the Coulomb repulsion and
reflected in the ballistic conductance. Here, many-body effects can still
affect electron occupations in the calculation of quantum ballistic conductance
although it cannot vary the center-of-mass velocity.
