Lund, 22nd - 24th January 2004
Quantum Ergodicity - Basic Ideas and Recent Developments
Scars on graphs
Holger Schanz (Göttingen)
A scar is a wavefunction with enhanced phase-space density in the
vicinity of an unstable periodic orbit. There is an established theory
of "weak scarring" (Heller et al.), where the enhanced probability
density is distributed over many states such that no particular state
deviates significantly from the ergodic limit. On the other hand, many
numerical experiments show "strong scars", where in one single state a
localization around a periodic orbit is clearly visible. A theory for
strong scarring in quantum graphs will be presented in the talk. It
shows that weak and strong scarring are completely unrelated
phenomena, at least for this particular model system.
[1] H. Schanz and T. Kottos: Scars on Quantum Networks Ignore the
Lyapunov Exponent,
Phys. Rev. Lett. 90 (2003) 234101.
Slides (pdf-file)
Workshop Home
Last modified: Feb 6 2004
Stefan Keppeler
(quantum.ergodicityATmatfys.lth.se)