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.... an AMS-IMS-SIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 19-23, 2005, ... 15 Form Factor Expansion for Large Graphs: a Diagrammatic Approach GREGORY BERKOLAIKO 35 The Spectral Form ... Local Spectral Density and Vacuum Energy Near a Quantum Graph Vertex STEPHEN A. FULLING 161 What Are Zeta ... For Quantum Star Graphs J.P. KEATING 191 Laplacians on Metric Graphs: Eigenvalues, Resolvents and Semigroupsanbsp;...
|Title||:||Quantum Graphs and Their Applications|
|Publisher||:||American Mathematical Soc. - 2006|