Resistance of a long wire in the quantum Hall regime

We study the two-probe transport in a long narrow channel of two-dimensional electron liquid (a quantum wire) in a strong magnetic field normal to the plane. The wire is split into alternating parallel strips of compressible and incompressible liquids. When the temperature is not too low, in every transverse cross section of the wire the electrochemical potential is different in different compressible strips but is uniform within each strip. The equilibration rate between two neighboring compressible strips falls off exponentially with the distance between them (the width of the separating incompressible strip). Assuming a parabolic confinement potential and small disorder potential, we find the magnetic-field dependence of the strip widths. Using only this dependence, we calculate the shape of the magnetoresistance peaks. We show that the low-field sides of these peaks are much steeper than the high-field sides, in agreement with recent experimental data.