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Quantum Graphs and Their Applications
 
Edited by: Gregory Berkolaiko Texas A&M University, College Station, TX
Robert Carlson University of Colorado, Colorado Springs, CO
Stephen A. Fulling Texas A&M University, College Station, TX
Peter Kuchment Texas A&M University, College Station, TX
Front Cover for Quantum Graphs and Their Applications
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Softcover ISBN: 978-0-8218-3765-8
Product Code: CONM/415
List Price: $103.00
MAA Member Price: $92.70
AMS Member Price: $82.40
Electronic ISBN: 978-0-8218-8094-4
Product Code: CONM/415.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $154.50
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AMS Member Price: $123.60
Front Cover for Quantum Graphs and Their Applications
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  • Front Cover for Quantum Graphs and Their Applications
  • Back Cover for Quantum Graphs and Their Applications
Quantum Graphs and Their Applications
Edited by: Gregory Berkolaiko Texas A&M University, College Station, TX
Robert Carlson University of Colorado, Colorado Springs, CO
Stephen A. Fulling Texas A&M University, College Station, TX
Peter Kuchment Texas A&M University, College Station, TX
Available Formats:
Softcover ISBN:  978-0-8218-3765-8
Product Code:  CONM/415
List Price: $103.00
MAA Member Price: $92.70
AMS Member Price: $82.40
Electronic ISBN:  978-0-8218-8094-4
Product Code:  CONM/415.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $154.50
MAA Member Price: $139.05
AMS Member Price: $123.60
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 4152006; 307 pp
    MSC: Primary 05; 11; 15; 28; 34; 35; 58; 60; 81;

    This volume is a collection of articles dedicated to quantum graphs, a newly emerging interdisciplinary field related to various areas of mathematics and physics. The reader can find a broad overview of the theory of quantum graphs. The articles present methods coming from different areas of mathematics: number theory, combinatorics, mathematical physics, differential equations, spectral theory, global analysis, and theory of fractals. They also address various important applications, such as Anderson localization, electrical networks, quantum chaos, mesoscopic physics, superconductivity, optics, and biological modeling.

    Readership

    Graduate students and research mathematicians interested in quantum graphs and application to number theory, mathematical physics, and other areas.

  • Table of Contents
     
     
    • Articles
    • Michael Aizenman, Robert Sims and Simone Warzel - Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs [ MR 2277604 ]
    • Matthew Baker and Xander Faber - Metrized graphs, Laplacian operators, and electrical networks [ MR 2277605 ]
    • Gregory Berkolaiko - Form factor expansion for large graphs: a diagrammatic approach [ MR 2277606 ]
    • Jens Bolte and Jonathan Harrison - The spectral form factor for quantum graphs with spin-orbit coupling [ MR 2277607 ]
    • Robert Carlson - Linear network models related to blood flow [ MR 2277608 ]
    • Kingwood Chen, Stanislav Molchanov and Boris Vainberg - Localization on Avron-Exner-Last graphs. I. Local perturbations [ MR 2277609 ]
    • Fan Chung and Ross M. Richardson - Weighted Laplacians and the sigma function of a graph [ MR 2277610 ]
    • Pavel Exner and Ondřej Turek - Approximations of permutation-symmetric vertex couplings in quantum graphs [ MR 2277611 ]
    • Daniel Fontaine, Thomas Smith and Alexander Teplyaev - Resistance of random Sierpiński gaskets [ MR 2277612 ]
    • Mark Freidlin and Matthias Weber - Small diffusion asymptotics for exit problems on graphs [ MR 2277613 ]
    • Leonid Friedlander - Determinant of the Schrödinger operator on a metric graph [ MR 2277614 ]
    • Stephen A. Fulling - Local spectral density and vacuum energy near a quantum graph vertex [ MR 2277615 ]
    • Matthew D. Horton, H. M. Stark and Audrey A. Terras - What are zeta functions of graphs and what are they good for? [ MR 2277616 ]
    • J. P. Keating - Fluctuation statistics for quantum star graphs [ MR 2277617 ]
    • Vadim Kostrykin and Robert Schrader - Laplacians on metric graphs: eigenvalues, resolvents and semigroups [ MR 2277618 ]
    • Stanislav Molchanov and Boris Vainberg - Transition from a network of thin fibers to the quantum graph: an explicitly solvable model [ MR 2277619 ]
    • Beng-Seong Ong - On the limiting absorption principle and spectra of quantum graphs [ MR 2277620 ]
    • Jacob Rubinstein - Quantum mechanics, superconductivity and fluid flow in narrow networks [ MR 2277621 ]
    • Holger Schanz - A relation between the bond scattering matrix and the spectral counting function for quantum graphs [ MR 2277622 ]
    • Uzy Smilansky and Michael Solomyak - The quantum graph as a limit of a network of physical wires [ MR 2277623 ]
    • B. Winn - On the trace formula for quantum star graphs [ MR 2277624 ]
  • Additional Material
     
     
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Volume: 4152006; 307 pp
MSC: Primary 05; 11; 15; 28; 34; 35; 58; 60; 81;

This volume is a collection of articles dedicated to quantum graphs, a newly emerging interdisciplinary field related to various areas of mathematics and physics. The reader can find a broad overview of the theory of quantum graphs. The articles present methods coming from different areas of mathematics: number theory, combinatorics, mathematical physics, differential equations, spectral theory, global analysis, and theory of fractals. They also address various important applications, such as Anderson localization, electrical networks, quantum chaos, mesoscopic physics, superconductivity, optics, and biological modeling.

Readership

Graduate students and research mathematicians interested in quantum graphs and application to number theory, mathematical physics, and other areas.

  • Articles
  • Michael Aizenman, Robert Sims and Simone Warzel - Fluctuation-based proof of the stability of ac spectra of random operators on tree graphs [ MR 2277604 ]
  • Matthew Baker and Xander Faber - Metrized graphs, Laplacian operators, and electrical networks [ MR 2277605 ]
  • Gregory Berkolaiko - Form factor expansion for large graphs: a diagrammatic approach [ MR 2277606 ]
  • Jens Bolte and Jonathan Harrison - The spectral form factor for quantum graphs with spin-orbit coupling [ MR 2277607 ]
  • Robert Carlson - Linear network models related to blood flow [ MR 2277608 ]
  • Kingwood Chen, Stanislav Molchanov and Boris Vainberg - Localization on Avron-Exner-Last graphs. I. Local perturbations [ MR 2277609 ]
  • Fan Chung and Ross M. Richardson - Weighted Laplacians and the sigma function of a graph [ MR 2277610 ]
  • Pavel Exner and Ondřej Turek - Approximations of permutation-symmetric vertex couplings in quantum graphs [ MR 2277611 ]
  • Daniel Fontaine, Thomas Smith and Alexander Teplyaev - Resistance of random Sierpiński gaskets [ MR 2277612 ]
  • Mark Freidlin and Matthias Weber - Small diffusion asymptotics for exit problems on graphs [ MR 2277613 ]
  • Leonid Friedlander - Determinant of the Schrödinger operator on a metric graph [ MR 2277614 ]
  • Stephen A. Fulling - Local spectral density and vacuum energy near a quantum graph vertex [ MR 2277615 ]
  • Matthew D. Horton, H. M. Stark and Audrey A. Terras - What are zeta functions of graphs and what are they good for? [ MR 2277616 ]
  • J. P. Keating - Fluctuation statistics for quantum star graphs [ MR 2277617 ]
  • Vadim Kostrykin and Robert Schrader - Laplacians on metric graphs: eigenvalues, resolvents and semigroups [ MR 2277618 ]
  • Stanislav Molchanov and Boris Vainberg - Transition from a network of thin fibers to the quantum graph: an explicitly solvable model [ MR 2277619 ]
  • Beng-Seong Ong - On the limiting absorption principle and spectra of quantum graphs [ MR 2277620 ]
  • Jacob Rubinstein - Quantum mechanics, superconductivity and fluid flow in narrow networks [ MR 2277621 ]
  • Holger Schanz - A relation between the bond scattering matrix and the spectral counting function for quantum graphs [ MR 2277622 ]
  • Uzy Smilansky and Michael Solomyak - The quantum graph as a limit of a network of physical wires [ MR 2277623 ]
  • B. Winn - On the trace formula for quantum star graphs [ MR 2277624 ]
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