Wavefunctions in chaotic quantum systems

• 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, ...