Introduction to Quantum Graphs (MAGIC039) |
GeneralDescription
During the last decade quantum graphs have become a paradigm model in
mathematics and physics. They combine the simplicity of one-dimensional wave
equations with a complex topology which allows to study many non-trivial phenomena
in spectral theory. This module will give an introduction to quantum
graphs, their spectra and their wavefunctions. Some applications in mathematical
physics and quantum chaos will be considered.
SemesterSpring 2013 (Monday, January 21 to Friday, March 29) Timetable
PrerequisitesQuantum Mechanics, Basics in Functional Analysis
SyllabusLaplacian on metric graph with Neumann (Kirchhoff) boundary conditions;
self-adjoint extensions of the Laplacian on a metric Graph; scattering
approach to quantum graphs, some spectral theory,
quantum-to-classical correspondence; trace formulae for the spectral counting function/density of states; spectral Statistics and Quantum Chaos on Quantum Graphs;
periodic-orbit theory for spectral correlations; wavefunctions on quantum graphs.
Lecturer
Students
Bibliography
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magic039exam
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