Lund, 22nd - 24th January 2004
Quantum Ergodicity - Basic Ideas and Recent Developments
Holger Schanz

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)

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