CONDENSATION OF STATES AND OSCILLATORY METAL-INSULATOR TRANSITIONS IN A MAGNETIC-FIELD

I reduce the eigenstates of the Schrodinger equation in a magentic field B and in an arbitrary set of scatterers to the eigenstates of an Hermitian matrix, which is presented by the explicit anlaytical formula. Its eigenstates prove that thermodynamics and transport in a random system in a magentic field qualitatively depend on the nature of scatterers. If they are short-range ones and there is less than one magnetic-flux quantum per scatterer, then a finite fraction of states condenses into narrow high-density-of-states bands in the vicinity of the Landau levels in vacuum. The states in these bands have high mobility in two dimensions and are extended in three dimensions. Magnetoresistance oscillates with magnetic field and may be nonmonotonic with temperature and impurity concentration.