Landau-level mixing and spin degeneracy in the quantum Hall effect

We study the dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing in a random intrachannel potential; the channels represent either two Landau levels or two spin states. We consider channel mixing as a function of the energy separation of the two extended states and show that its effect changes from repulsion to attraction as the energy separation increases. For two Landau levels this leads to level floating at low magnetic fields, while for Zeeman-split spin states we predict level attraction at high magnetic fields, accounting for electron spin resonance data. We also study random mixing of two degenerate channels, while the intrachannel potential is periodic (nonrandom). We find a single extended state with a localization exponent \ensuremath{\nu}\ensuremath{\approx}1.1 for real scattering at nodes; the general case also has a single extended state, though the localized nature of nearby states sets in at unusually large scales.