Introduction to Quantum Graphs (MAGIC039)
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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.
Spring 2013 (Monday, January 21 to Friday, March 29)
Quantum Mechanics, Basics in Functional Analysis
Laplacian 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.
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The Assessment for this course will be via a take-home examination, which will be made available shortly after the end of the course. The examination will consists of 2 parts. Both should be fully answered. Part 1 contains 3 questions and part 2 contains two questions. The total mark is 50 and the pass mark is 25.
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