MAGIC039: Introduction to Quantum Graphs

Course details

Semester

Monday, January 11th to Friday, March 19th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Description

Contents:
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.


Syllabus: 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; level spacing distribution; periodic-orbit theory for spectral correlations; wavefunctions on quantum graphs.


Prerequisites: Quantum Mechanics, Basics in Functional Analysis


Literature:
  • S. Gnutzmann and U. Smilansky: Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics, Advances in Physcs 55, 527 (2006).
  • T. Kottos and U. Smilansky: Periodic Orbit Theory and Spectral Statistics for Quantum Graphs, Annals of Physics 274, 76 (1999)
  • P. Kuchment,Quantum graphs I. Some basic structures, Waves in Random Media 14, S107 (2004).

Prerequisites

No prerequisites information is available yet.

Syllabus

No syllabus information is available yet.

Lecturer

  • SG

    Dr Sven Gnutzmann

    University
    University of Nottingham

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Assessment

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