Introduction to quantum graphs
Gregory Berkolaiko, Peter Kuchment
- Providence: American Mathematical Society, 2013
- xiii, 270 p. grap0hs 27 cm.
- Mathematical surveys and monographs ; volume 186 .
Anexe p. 209 Bibliografie p. 227 Index p. 267
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.
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.