Introduction to Quantum Graphs

Gregory Berkolaiko, Peter Kuchment

ISBN: 9781470425999 | Year: 2016 | Paperback | Pages: 288 | Language : English

Book Size: 180 X 240 mm | Territorial Rights: Restricted| Series American Mathematical Society

Price: 960.00

About the Book

A “quantum graph” is a graph considered as a one-dimensional complex and equipped with a differential operator (“Hamiltonian”). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., “meso-” or “nano-scale”) system that looks like a thin neighborhood of a graph. Since at least the 1930S, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications<

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

Gregory Berkolaiko is Professor at the Department of Mathematics, Texas A&M University, College Station, USA.

Peter Kuchment is University Distinguished Professor at the Department of Mathematics, Texas A&M University, College Station, USA.

Table of Contents

Chapter 1. Operators on Graphs  
Chapter 2. Quantum Graph Operators 
Chapter 3. Spectra of Quantum Graphs 
Chapter 4. Spectra of Periodic Graphs 
Chapter 5. Spectra of Quantum Graphs 
Chapter 6. Quantum Chaos on Graphs 
Chapter 7. Some Applications and Generalizations 
Appendix A. Some Notions of Graph Theory 
Appendix B. Linear Operators and Operator-Functions 
Appendix C. Structure of Spectra 
Appendix D. Symplectic Geometry and Extension Theory