A duality between Schroedinger operators on graphs and certain Jacobi matrices

TL;DR

This paper extends the known relationship between Schroedinger operators on graphs and Jacobi matrices, covering a broader class of models including lattices with magnetic fields and comb-shaped graphs, revealing a duality in spectral analysis.

Contribution

It introduces a generalized duality between Schroedinger operators on graphs and Jacobi matrices, expanding the scope of models where this correspondence applies.

Findings

Extended the duality to rectangular lattices with magnetic fields

Included comb-shaped graphs in the duality framework

Provided new insights into spectral properties of graph-based Schroedinger operators

Abstract

The known correspondence between the Kronig-Penney model and certain Jacobi matrices is extended to a wide class of Schroedinger operators on graphs. Examples include rectangular lattices with and without a magnetic field, or comb-shaped graphs leading to a Maryland-type model.