CONDENSATION OF STATES AND OSCILLATORY METAL-INSULATOR TRANSITIONS INA MAGNETIC-FIELD

I reduce the eigenstates of the Schrodinger equation in a magentic fie ld B and in an arbitrary set of scatterers to the eigenstates of an He rmitian matrix, which is presented by the explicit anlaytical formula. Its eigenstates prove that thermodynamics and transport in a random s ystem in a magentic field qualitatively depend on the nature of scatte rers. If they are short-range ones and there is less than one magnetic -flux quantum per scatterer, then a finite fraction of states condense s into narrow high-density-of-states bands in the vicinity of the Land au levels in vacuum. The states in these bands have high mobility in t wo dimensions and are extended in three dimensions. Magnetoresistance oscillates with magnetic field and may be nonmonotonic with temperatur e and impurity concentration.