Quantum graph models of quantum chaos: an introduction and some recent applications

TL;DR

This paper introduces quantum graphs as models for quantum chaos and spectral theory, summarizing key results and recent developments in the field.

Contribution

It provides a concise didactical overview of quantum graphs, highlighting recent advances and foundational results in quantum chaos and spectral analysis.

Findings

Summarizes seminal results in quantum graphs and quantum chaos.

Provides an overview of recent developments in the field.

Highlights the role of periodic orbit theory in spectral analysis.

Abstract

Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to quantum chaos, periodic orbit theory and spectral theory. We summarise related seminal results, and give an overview over a few more recent developments.