Localization in a quasiperiodic model on quantum graphs

TL;DR

This paper demonstrates that quantum graphs with Maryland-type quasiperiodic Kirchhoff coupling constants exhibit a dense pure point spectrum, advancing understanding of spectral properties in quasiperiodic quantum graph models.

Contribution

It establishes the existence of a dense pure point spectrum in a specific quasiperiodic quantum graph model, which was previously unproven.

Findings

Presence of dense pure point spectrum on the quantum graphs.

Spectral properties influenced by Maryland-type quasiperiodic couplings.

Advancement in understanding spectral behavior in quasiperiodic quantum systems.

Abstract

We show the presence of a dense pure point spectrum on quantum graphs with Maryland-type quasiperiodic Kirchhoff coupling constants at the vertices.