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

Quantum Ergodicity - Basic Ideas and Recent Developments
Pseudo-integrable systems classically have properties that are intermediate between integrable and chaotic systems: their periodic trajectories occur in pencils of periodic orbits, but singularities can split these pencils, yielding an indetermination at the boundary between the pencils. These mixed classical characteristics have their quantum counterpart: the quantum energy spectrum displays statistics which are intermediate between the statistics of integrable and chaotic systems: the nearest-neighbour spacing distribution shows level repulsion at the origin and exponential decrease at infinity; the spectral form factor is intermediate between 0 (chaotic case) and 1 (integrable case) at infinity. We will give several examples where it is possible to calculate analytically these quantities.

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