Localization for a class of discrete long-range quasi-periodic operators.

In this paper we study discrete quasi-periodic operators with certain long-range hopping and monotonic meromorphic potentials. The hopping amplitude decays with the interparticle distance | n | as e - r log t (1 + | n |) ( t > 1 , r > 0 , n ∈ Z v ). By employing the KAM method, we prove such operators have pure point spectrum with eigenfunctions φ i i ∈ Z v obeying φ i (n) ≤ 2 e - r 2 log t (1 + | n - i |) for all i ∈ Z v , n ∈ Z v . [ABSTRACT FROM AUTHOR]