Wavefunction Statistics using Scar States

Details Wavefunction Statistics using Scar States Wavefunction Statistics using Scar States

2003-04-11

arxiv.org/abs/nlin/0304018v1

Ann. Phys. (N.Y.), vol. 307, pp 392-420 (2003)

Nonlinear Sciences

Chaotic Dynamics

31 pages, 11 figures, to appear in Annals of Physics

Scientific paper

10.1016/S0003-4916(03)00081-2

We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and provide a natural means of characterising scarring effects in individual wavefunctions as well as their collective statistical properties. In particular, these states may be used to find scarring in regions of the spectrum normally associated with antiscarring and suggest a characterisation of templates for scarred wavefunctions which vary over the spectrum. The results are applied to quantum maps and billiard systems.

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