A Series of Spectral Gaps for the Ganeshan–Pixley–Das Sarma Model

We study a one-dimensional quasiperiodic difference Schrödinger operator with a potential obtained by restricting a certain meromorphic function to the integer lattice. Assuming that the coupling constant is sufficiently small, we asymptotically describe a series of intervals contained in spectral gaps, their centers, and lengths. The lengths of these intervals decrease exponentially as their number increases, and the rate of their decrease is determined by the distance from the poles of the potential to the real axis.

DOI 10.1134/S1061920824040046