Phase transitions in the quantum Hall liquid in a quantum wire

Two scenarios for the collapse of the ν=1 quantum Hall liquid (QHL) state, with the effective quantum wire (QW) width defined by the Fermi vector kF, are studied. Here, ν for the QW is defined as the filling factor of Landau levels (LL) at the center of the QW. In the first one there is no electron redistribution at critical magnetic field Bcr(1), where the Fermi energy, EF, coincides with the bottom of the empty upper spin-split LL. For B