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General


Description

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.

Semester

Spring 2013 (Monday, January 21 to Friday, March 29)

Timetable

  • Tue 11:05 - 11:55

Prerequisites

Quantum Mechanics, Basics in Functional Analysis

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; periodic-orbit theory for spectral correlations; wavefunctions on quantum graphs.

Lecturer


Sven Gnutzmann
Email sven.gnutzmann@nottingham.ac.uk
Phone (0115) 9514924
Interests quantum-to-classical correspondence, quantum graphs, quantum billiards, nodal patterns
Photo of Sven Gnutzmann


Students


Photo of David Matthews
David Matthews
(Southampton)
Photo of Adam  Newman
Adam Newman
(Loughborough)
Photo of Yafet Sanchez Sanchez
Yafet Sanchez Sanchez
(Southampton)


Bibliography


Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics.Gnutzmann and Smilansky
Periodic Orbit Theory and Spectral Statistics for Quantum Graphs.Kottos and Smilansky
Quantum graphs: I. Some basic structuresKuchment


Note:

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Assessment



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.

magic039exam

Files:Exam paper
Deadline: Thursday 25 April 2013 (1611.6 days ago)
Instructions:

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.



Recorded Lectures


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