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Introduction to Quantum Graphs
 
Gregory Berkolaiko Texas A&M University, College Station, TX
Peter Kuchment Texas A&M University, College Station, TX
Introduction to Quantum Graphs
Hardcover ISBN:  978-0-8218-9211-4
Product Code:  SURV/186
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-9455-2
Product Code:  SURV/186.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-9211-4
eBook: ISBN:  978-0-8218-9455-2
Product Code:  SURV/186.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Introduction to Quantum Graphs
Click above image for expanded view
Introduction to Quantum Graphs
Gregory Berkolaiko Texas A&M University, College Station, TX
Peter Kuchment Texas A&M University, College Station, TX
Hardcover ISBN:  978-0-8218-9211-4
Product Code:  SURV/186
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-9455-2
Product Code:  SURV/186.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-9211-4
eBook ISBN:  978-0-8218-9455-2
Product Code:  SURV/186.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1862013; 270 pp
    MSC: Primary 34; 35; 81; 58; 05; 82; 47

    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. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc.

    Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory.

    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.

    Readership

    Graduate students and research mathematicians interested in this new area of mathematics and its applications.

  • Table of Contents
     
     
    • Chapters
    • 1. Operators on graphs. Quantum graphs
    • 2. Quantum graph operators. Special topics
    • 3. Spectra of quantum graphs
    • 4. Spectra of periodic graphs
    • 5. Spectra of quantum graphs. Special topics
    • 6. Quantum chaos on graphs
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1862013; 270 pp
MSC: Primary 34; 35; 81; 58; 05; 82; 47

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. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc.

Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory.

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.

Readership

Graduate students and research mathematicians interested in this new area of mathematics and its applications.

  • Chapters
  • 1. Operators on graphs. Quantum graphs
  • 2. Quantum graph operators. Special topics
  • 3. Spectra of quantum graphs
  • 4. Spectra of periodic graphs
  • 5. Spectra of quantum graphs. Special topics
  • 6. Quantum chaos on graphs
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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