Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

摘要: The Schrodinger difference operator considered here has the form $$(H_\varepsilon (\alpha )\psi )(n) = - (\psi (n + 1) \psi 1)) V(n\omega \alpha (n)$$ whereV is aC2-periodic Morse function taking each value at not more than two points. It shown that for sufficiently smallɛ operatorHɛ(α) a.e.α a pure point spectrum. corresponding eigenfunctions decay exponentially outside finite set. integrated density of states an incomplete devil's staircase with infinitely many flat pieces.