Quasiperiodic surface Maryland models on quantum graphs

TL;DR

This paper investigates the spectral properties of quantum graphs with quasiperiodic couplings, revealing how the transition between absolutely continuous and pure point spectra is controlled by an associated Hill operator.

Contribution

It introduces a novel analysis of quantum graphs with quasiperiodic surface Maryland model couplings, linking spectral transitions to Hill operators.

Findings

Spectral types are characterized for the quantum graphs studied.

The transition between spectral types is governed by the Hill operator.

The spectral analysis connects quasiperiodic couplings with classical differential operators.

Abstract

We study quantum graphs corresponding to isotropic lattices with quasiperiodic coupling constants given by the same expressions as the coefficients of the discrete surface Maryland model. The absolutely continuous and the pure point spectra are described. It is shown that the transition between them is governed by the Hill operator corresponding to the edge potential.