Exchange interaction in a quantum wire in a strong magnetic field

We show that, for a sufficiently high number of electrons per unit length, the lateral confinement in narrow wires restores degeneracies that are lifted by exchange effects in two-dimensional systems in a magnetic field. The results are used to explain some experimental observations where the two-probe conductance of a quantum wire was found to be quantized with step size 2${\mathit{e}}^2$/h.