Introduction to quantum graphs /

Introduction to quantum graphs / Gregory Berkolaiko, Peter Kuchment.

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Bibliographic Details
Main Author:	Berkolaiko, Gregory, 1976-
Other Authors:	Kuchment, Peter, 1949-
Format:	Book
Language:	English
Published:	Providence, Rhode Island : American Mathematical Society, [2013]
Series:	Mathematical surveys and monographs ; no. 186.
Subjects:	Quantum graphs. Boundary value problems. Combinatorics > Graph theory > Graphs and linear algebra (matrices, eigenvalues, etc.) Ordinary differential equations > Boundary value problems > Boundary value problems on graphs and networks. Partial differential equations > Spectral theory and eigenvalue problems > Spectral theory and eigenvalue problems. Partial differential equations > Miscellaneous topics > Partial differential equations on graphs and networks (ramified or polygonal spaces) Operator theory > Miscellaneous applications of operator theory > Applications in chemistry and life sciences. Global analysis, analysis on manifolds > Partial differential equations on manifolds; differential operators > Spectral problems; spectral geometry; scattering theory. Quantum theory > General mathematical topics and methods in quantum theory > Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. Quantum theory > General mathematical topics and methods in quantum theory > Quantum chaos. Statistical mechanics, structure of matter > Applications to specific types of physical systems > Superconductors. Statistical mechanics, structure of matter > Applications to specific types of physical systems > Quantum wave guides, quantum wires. Statistical mechanics, structure of matter > Applications to specific types of physical systems > Nanostructures and nanoparticles.

Table of Contents:

Operators on graphs : quantum graphs
Quantum graph operators : special topics
Spectra of quantum graphs
Spectra of periodic graphs
Spectra of quantum graphs : special topics
Quantum chaos on graphs
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.