ELECTRON ON A LATTICE IN A MAGNETIC-FIELD

I consider an electron on a 2D lattice of arbitrary short-range scatte rers in magnetic field. I accurately reduce its Schroedinger equation to an explicit Hermitian matrix. If the number phi of magnetic-flux qu anta per site is less than one, then similar or equal to (1 - phi)-th fraction of all states condenses into narrow high-density-of-states ba nds in the vicinity of Landau levels. Point scatterers shrink these ba nds into infinitely degenerate Landau levels. The states in the bands have high mobility in two and are extended in three dimensions. Magnet oresistance oscillates with magnetic field and may be non-monotonic wi th temperature and impurity concentration.