On the limiting absorption principle and spectra of quantum graphs

TL;DR

This paper proves the limiting absorption principle for certain quantum graphs, showing the absence of singular continuous spectrum by using Dirichlet-to-Neumann operators, advancing understanding of spectral properties of quantum graphs.

Contribution

It establishes the limiting absorption principle for quantum graphs with infinite leads, a novel result using Dirichlet-to-Neumann operators.

Findings

Validates the limiting absorption principle for specific quantum graphs.

Shows absence of singular continuous spectrum in these graphs.

Introduces a technique involving Dirichlet-to-Neumann operators.

Abstract

The main result of the article is validity of the limiting absorption principle and thus absence of the singular continuous spectrum for compact quantum graphs with several infinite leads attached. The technique used involves Dirichlet-to-Neumann operators.