Lund, 22nd - 24th January 2004
Quantum Ergodicity - Basic Ideas and Recent Developments
Periodic orbits and spectral statistics of pseudo-integrable systems
Olivier Giraud (Bristol)
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.
Slides (gzipped postcript-file)
Workshop Home
Last modified: Jan 28 2004
Stefan Keppeler
(quantum.ergodicityATmatfys.lth.se)