On nonperturbative localization with quasi-periodic potential

摘要: The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators quasi-periodic potentials d frequencies. First, in case = 1 or 2, it is proved that spectrum pure-point exponentially decaying eigenfunctions all (defined terms a trigonometric polynomial on d-dimensional torus) which Lyapounov exponents strictly positive frequencies and energies. Second, every non-constant real-analytic potential Diophantine set frequencies, lower bound given same rescaled by sufficiently large constant.