Lund, 22^{nd} - 24^{th} January 2004

Quantum Ergodicity - Basic Ideas and Recent Developments
In this course we give an introduction to the behaviour of wavefunctions in chaotic systems.

Topics:

- classical billiards: examples, ergodicity, mixing, periodic orbits
- quantum billiards: examples, spectral staircase function, eigenfunctions in integrable vs. chaotic systems, mean behaviour of eigenfunctions, statistical properties of wave functions (random wave model)
- quantum ergodicity: semiclassical eigenfunction hypothesis, quantum ergodicity theorem (+ a sketch of the mathematical background), simple examples, quantum limits, bouncing ball modes, scars rate of quantum ergodicity
- More recent topics: autocorrelation function and quantum ergodicity, quantum ergodicity for Poincaré Husimi functions, ...

Slides (pdf-file, 5.5MB)

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Last modified: Jan 28 2004 Stefan Keppeler (